57min30sec
1. (R' D R)
2. (U L2)
3. (B)
4. L' D' L2 U2
5. (U F2 U')
6. (R' F' R' F)
7. (R) {3e/3'1'c}@[18]
Found:
3-0: U2 [F' D' F D] U2 -> {3'1'c}@[23]
4-1: B D L2 [B' R' B R] L2 D' B' -> {3c}@[28]

Felt these were pretty equivalent, but had some time for {3'1'c} and felt as long as I could get <[5] -> {3c} it was worthwhile.
Sure enough, found:
2-2: U L U' R2 U L' U' R2 -> {3c}@[27] and then figured I better wrap things up and took:
7-1: R D' L' D R' D' L D -> {}@[33]

58min20sec
1. L2 F D2
2. B2 U2
3. F2 R2 F
4. B
5. (R D' R') {2'1'e/4'1'c}@[12]
6. (D' B D' B' D) {3e/22c}@[17]
Alt.
4. B' D R' B R
5. D' B D B {3e/31'1'c}@[17]

Went for {2'1'e/4'1'c}@[12] and found:
5-1: L2 U' [F'] U L2 {3e/5c}@[17]
2-0: U' B' [U'] B U {3e/3'1'c}@[17]

Took {3e/5c}@[17], but only found 2-0: F' [U B L B' L' U'] F -> {5c}@[25]
Short on time, but was a bit lucking in quickly finding +[6]+[5] -> {}.
5-1-4: U L D L' U' L D' L' +[6] -> {3c}
5-1-2: U L' U' R' U L U' R +[5] -> {}

55min30sec
1. R B' F L' F'
2. (U L' U2 B' U' B')
3. (U B' U B)
4. U2
5. U L2 U' L {3e/5c}@[19]
Alt.
5. U L2 U' L' {3e/5c}@[19]
Went for first one found:
2-6: +[9] -> {5c}
2-5: +[5] -> {5c}
2-3: +[9] -> {3c}
2-1: B [F U F' U'] B' +[5] -> {3c}
Then {3c} +[7] -> {} was the best I could find: 5-1: U2 R D' R' U2 R D R'

Went back to 2nd {3e/5c} case and found +[6] -> {3c} figured this was decent since as long as I had less than +[6] -> {} it would be better, but was basically out of time. I was only able to find net [6] 3c-cycles in overtime.

57min50sec
1. R
2. (U)
3. (D2 F L' F2)
4. L' F2
5. R B R2 B {31'1'e/3'1'c}@[12]
Alt.
5. R2
6. (R B' R')
7. (D B' D')
8. (R D' R' D B) {3e/3'1'c}@[20]
Alt.
7. (R' B' R) {21'1'e/4'1'c}@[14]
8. (B) {22e/2'2'1'c}@[15]
Alt.
8. (B') {22e/5c}@[15]

Went for the last {22e/5c}@[15] case. Theoretically would have checked them both out, but too time consuming.
3-0: U' B D [B2] D' B' U -> {5c}@[22] +[6]+[4] -> {}

Don't care to continue in overtime. This was a mess: can't properly count moves, can't turn the cube properly, can't write moves down properly....should've been able to at least salvage something in the high 30s, but messed that up.

56min50sec
1. D2 F' D U' R' D2
2. U R B R
3. D' L2 B D2 B'
4. B' L' B L {3e/3'1'c}@[18]
5. L' B D L D' L' B'
6. L {5c}@[23]
Started with {3e/3'1'c} case and best I could find is:
3-3: U2 R U' R' [R D R' D'] R U R' U2 -> {3c}@[28]
Checked {5c} case and worked from end of skeleton back to 2-2, but best I found was +[6]+[6] -> {}
Since even a 7-mover on top of {3c}@[28] would tie this, I decided in the interest of time I should just go back to that case and found:
3-3-11: B U B' D2 B U' B' D2 -> {}@[34]

46min40sec
1. B2 U L2 B' D
2. (F B2 D')
3. (R2)
4. F R' F' R2 {3'1'e/5c}@[11]
5. (D R' D' R) {3e/3'1'c}@[16]
Alt.
5. F2 D' F D F' {3e/3c}@[18]
Alt.
5. F D' F2 D F {3e/3c}@[18]
6. F' D F R F' R' D' F {3c}@[23]

Decided to just secure something decent with {3c}@[23] and quickly found 6-7: D R D' L D R' D' L' -> {}@[27]
Then explored both {3e/3c} cases and couldn't find anything better than net [6] -> {3c} so then just did a full search on the {3c}; i.e., normal skeleton through step 6, but didn't find anything better than the net [4] at 6-7.

Had plenty of time, and in hindsight, I should have explored {3e/3'1'c}@[16], because all these cases I was looking at were similar and {3e/3'1'c}@[16] still has some potential, but my initial misjudgement was that {3e/3c}@[18] vs. {3e/3'1'c}@[16] was like having a 2-move 3c-cycle, but in reality, I would be looking for something like {3e/3'1'c} -> {3c} in [4-6]ish which would have been better than {3c}@[23]. I think I'm going to explore this in overtime.

1. B2 U L2 B' D
4. F R' F' R
5. D R D'
3. R2
2. D B2 F'

5-0: D' [L' F L F'] D -> {3c}@[21]
5-2: R' D' R U' R' D R U -> {}@[26]

Well that's what I was able to find. Too bad, but that's why it's important to work through these things so we remember our mistakes better and can learn from them.

46min40sec
1. B2 U L2 B' D
2. (F B2 D')
3. (R2)
4. F R' F' R2 {3'1'e/5c}@[11]
5. (D R' D' R) {3e/3'1'c}@[16]
Alt.
5. F2 D' F D F' {3e/3c}@[18]
Alt.
5. F D' F2 D F {3e/3c}@[18]
6. F' D F R F' R' D' F {3c}@[23]

Decided to just secure something decent with {3c}@[23] and quickly found 6-7: D R D' L D R' D' L' -> {}@[27]
Then explored both the {3e/3c} cases and couldn't find anything better than net [6] -> {3c} so then just did a full search on the {3c}; i.e., normal skeleton through step 6, but didn't find anything better than the net [4] at 6-7.

Had plenty of time, and in hindsight, I should have explored {3e/3'1'c}@[16], because all these cases I was looking at were similar and this one still has some potential, but my initial misjudgement was that {3e/3c}@[18] vs. {3e/3'1'c}@[16] was like having a 2-move 3c-cycle, but in reality, I would be looking for something like {3e/3'1'c} -> {3c} in [4-6]ish which would have been better than {3c}@[23]. I think I'm going to explore this in overtime.

58min00sec
{4e/2'1'c}@[20] vs. {3e/3'1'1'c}@[20] vs. {4e/2'1'c}@[19] vs. {3e/5c}@[21]

First checked out {4e/2'1'c}@[19] but didn't find anything promissing
For {3e/5c} found:
+[7] -> {3c}
+[4] -> {5c}
+[5] -> {3c} +[7] -> {}

Went back to see if I gould find a really good 3c-cycle for the +[7] -> {3c} case, but there was practically nothing.

59min10sec
1. B' U D' F' D2
2. L D F' U2
3. D' F
4. (F2 L F U' F')
5. U L2 B L2 B' L2 {3e/5c}@[22]
6. U B L B' L' U' {3c}@[28]

Secured a [36] by just finding a 3c-cycle in the last normal session, then explored {3e/5c} case, but didn't find anything worthwhile so went back to {3c}@[28] and was only able to find +[7] -> {}. Thought I found a 6 mover, but made a misturn somewhere so I didn't really properly check part of the skeleton, but I just wanted to get this down in time, and it's not worth going back to properly check for what is probably only going to be worth a move or two better at most.

50min30sec
1. U2
2. (U2 F2)
3. (U R U)
4. (F' R2 F D')
5. (R2 D' R) {3e/5c}@[13]
In normal skeleton:
1-0: B2 U B2 [D F D' F'] B2 U' B2 -> {3c}@[23]
1-0-2: U' B U F2 U' B' U F2 -> {}@[28]

I actually had a ton of extra time here and went back to see if I could make one big insertion for {3e/5c} -> {} but couldn't come up with anything better. What I should have done is searched in the last 12 moves of the inverse space session, but I normally don't bother doing this because I usually don't have such a long session and therefore it typically requires stickering up another cube just to check a few configurations, so I've almost completely forgotten this is an option.

58min00sec
Well this was a mad dash to get something because I spent a lot of time to end up with a {3e/3'1'1'c}@[21] skeleton and decided to just try something completely different with <30min left. I was able to get:
1. F
2. B2 U B'
3. D F' U2
4. (B2 D')
5. (B L)
6. (D' B D)
7. (L U' L' U B2) {3e/3'1'c}@[19] meh!
Alt.
7. B' U B' U' {3e/2'2'c}@[18]
But I was pressed for time and couldn't really explore this very well, so I just took
4-1: D U' L2 D' U B2 +[3] -> {2'2'c} and then whatever decent 3c-cyles I could find: +[5]+[7] -> {}

57min40sec
1. R
2. B2 R U2
3. (B)
4. (F2 R2)    Alt. (R2 F2 R2 F2 R) {3e/2'2'1'1'c} @[10]?
5. R D R2 D'
6. F U F U' F2 {3e/3c}@[16]     Alt. U F2 U' F2 {3e/2'21'c}@[15]
7. D' F' L' F L D {3c}@[22]
8. D2 R2 D L D' R2 D L' D {}@[30]
Worked with {3e/3c}@[16] to see if there was <[6] to {3c}.
Found 6-4: U' F' R' F R U -> {3c}@[21]. I suppose I should have been able to figure this out since my last layer was the F-face, and this is what I would have done with normal solving if I fixed edges before the final F2 turn, but anyway, it saved me a move, and I was feeling pretty good even with +[8] -> {}, which could be done at the end of the skeleton, but I found +[7], then +[6], and then +[5], and got really luck with:
2-1: B2 R F' R' B2 R F R' +[3] -> {}

Played around with the {3e/2'2'1'1'c} case a bit after submission, but am not seeing anything worthwhile.

57min00sec
1. F'
2. (F' L2 D')
3. (B R U R2)
4. (B U)
5. R2 U' B' R' B' {2'21'e/3e}@[15]
6. R B U' B' U R {3e/3'1'1'c}@[21]
Went for {2'21'e/3e}.
1-0: L U2 [R2] U2 L' -> {3e/5c}@[20]
5-3: [L B U B' U' L'] -> {3c}@[26]
2-3: F' L F R F' L' F R' -> {}@[31]

53min20sec
I created a real mess for myself here, but really wanted to explore this idea I've contemplated from time to time.
1. B R2 B
2. L' U' F U F2 {4e/6c}@[8]
This isn't the full manifestation of the approach because the approach itself is too time consuming for me, but in short:
(a) sticker up the entire cube with all the cycles needed to solve at the very beginning
(b) look for some short set of moves that solves a handful of pieces
(c) the moves in (b) become the skeleton, and one just keeps looking for insertions for the remaining pieces, re-stickering the cube as necessary

Nonetheless, I found having 10 pieces solved in 8 moves to be decent. Then I found
3. D [R'] D' {4e/6c} -> {3e/7c}, not really better, but at least it gets it in terms of cycles I can deal with.
Then I ended up taking a 12 mover to get to {5c} which isn't great, but {5c}@[23] isn't a total disaster for me:
2-3: R2 B' L2 B2 [F R F' R'] B2 L2 B R2
Thought I had found a 6-mover to {7c}, but I messed something up. In essense that was postentially better because with {7c} there's a high probability of having a pretty good 3c insertion somewhere in the skeleton. Anyway, at that point I just wanted to finish so I don't DNF the weekly and finished with +[5]+[7] for {5c} -> {}.

Okay, I played around with this some more and the best I could find in a reasonable amount of time was:
2-2: {4e/6c} -> {5c}@[18] U' L2 R' F U' [L'] U F' R L2 U
Then did a full search for {5c} -> {} and best compatible pair of 3c cycles I could find were +[5]+[8].

53min20sec
I created a real mess for myself here, but really wanted to explore this idea I've contemplated from time to time.
1. B R2 B
2. L' U' F U F2 {4e/6c}@[8]
This isn't the full manifestation of the approach because the approach itself is too time consuming for me, but in short:
(a) sticker up the entire cube with all the cycles needed to solve at the very beginning
(b) look for some short set of moves that solves a handful of pieces
(c) the moves in (b) become the skeleton, and one just keeps looking for insertions for the remaining pieces, re-stickering the cube as necessary

Nonetheless, I found having 10 pieces solved in 8 moves to be decent. Then I found
3. D [R'] D' {4e/6c} -> {3e/7c}, not really better, but at least it gets it in terms of cycles I can deal with.
Then I ended up taking a 12 mover to get to {5c} which isn't great, but {5c}@[23] isn't a total disaster for me:
2-3: R2 B' L2 B2 [F R F' R'] B2 L2 B R2
Thought I had found a 6-mover to {7c}, but I messed something up. In essense that was postentially better because with {7c} there's a high probability of having a pretty good 3c insertion somewhere in the skeleton. Anyway, at that point I just wanted to finish so I don't DNF the weekly and finished with +[5]+[7] for {5c} -> {}.

51min10sec
1. F
2. (B2)
3. (U' F2 L')
4. (B2 U R')
5. R2
6. U2
7. (R B2 L' B L B' R' B') {3e/3'1'c}@[18]
Alt.
7. (B L' B2 L R B' R') {4e/4'1'c}@[17]
8. (B) {3e/5c}@[18]
Alt.
7. (B2 L' B L)
8. (R B' R' B) {3e/5c}@[18]

Went with last {3e/5c} option, in normal skeleton found:
2-1: U' [R' D R D'] U -> {3c} +[6]
8-3: B L B' R2 B L' B' R2 -> {} +[6]

Tempting to see if I may have gotten lucky with {4e/4'1'c}@[17], say net [5]ish -> {3c}, and I had a little extra time where I could have tried to check this out quickly, but being pressed for time, I probably would have messed something up anyway.

This maybe had some potential, but a lot of option to have to explore, and I just messed up and ran out of time in the end.
{22e/2'2'c} [20]
Found
net [1] -> {3e/5c}
net [5] -> {5c}
net [0] -> {3e/5c} then a net [4] -> {5c} but in the interest of time, I should have just taken the {5c}@[25], and there are still a lot of things to look for in a {22e/2'2'c case} that I just don't have the ability to focus on them all simultaneously, so it takes forever.

1. L2 D B2
2. R2 F' L
3. B D B2
4. D' R
5. (R2 D2 R) {3'1'c/5c}@[11]

1. L2 D B2
2. R2 F' L
3. B D B2
4.
5. D R2
5-2: R' U L [D2 F D2 F'] L U R {3e/3c}@[20]
or
3-1: R' [F D F' D'] R {3e/5c}@[17], went for this over the prior one

1-0: R2 U2 [D2 B D2 B'] U2 R2 -> {3c}@[25]
1-0-4: B D' F' D B' D' F D -> {}@[31]

Just got this corrected with 1 second left!
Not bad for kind of a disaster of a solution.
{3e/2'2'c} @[17] couldn't really find anything, but I forget how flexible this configuration can be because I remain very fixated on solving the unsolved corners, but it is also very appropriate for my insertion to only involve say 3 of the 4 corners and just create an extra unsolved corner resulting in a {5c} case, or maybe just solving one corner but adding an unsolved one as I found a net [5] to {3'1'c} and was then able to find +[5]+[5] -> {}. If I can remember to consider these options, then this may more easily result in some < net [4] move insertions to solve the edges without making the corner situation worse.
1. R
2. B' L' F2
3. R' D2
4. F
5. (F)
6. (L B L B')
7. (L' U' L2)
8. (L U2 L')

In normal space skeleton:
7-1: F' [F' D F D'] F -> {3'1'c}
5-1: F L' B' L F' L' B L -> {3c}
8-3: L' U' L D L' U L D'

I initially wrote this last one down with U and U' interchanged, which is the last second correction I was able to make and avoid a DNF.

1. (F' L F2)
2. (U' L2)
3. (R F D2)
4. R U F2 U'
5. R2 F' R
6. F' R2 {3e/2'2'c} @[17]
Alternates:
6. (R2) {4e/21'1'c} @[15]
7. (F') {3e/22c} @[17]
7. (F) {3e/2'2'c) @[17]

Went with first {3e/2'2'c} @[17]
5-1: R F2 F' F2  +[2] -> {5c} +[7]+[6] -> {}
Can't complain about {3e/2'2'c} -> {5c} in net [2], but hoped for better than +[13] on the {5c}. Who knows, if I actually had time to fully check it out, perhaps I would have found something in fewer moves.

{3e/22c}@[21] +[5] -> {2'2'c} +[4]+[7] -> {}

Well, that ended up being okay as a mad dash just to get something after struggling with the skeleton and making all sorts of turning errors.
{3e/5c}@[22] +[9] -> {3c} +[4] -> {}

Initially was going to go with a {3e/5c} +[7] -> {5c}@[29], but took my chances with a few extra moments to look for something better.

1. F2 U L'
2. R2 U2
3. F2 L2 F2
4. L
5. (L D2 L)
6. (F' D2 F)
7. (D) {3e/31'1'1c} @[16]
Alt.
7. (D') {3e/5c} @[16]
Alt.
6. (D' F' D' F D') {3e/2'2'2c} @[17]

Went with {3e/2'2'c}, @4-0 found: D2 B R2 U [D' L D L'] U' R2 B' D2 -> {} @[29]
Thought I found a way to do the same nearby with net [10] instead of net [12] but must have messed something up because I couldn't reproduce it. I was hoping to have some time to explore {3e/5c}@[16] case, but ended up wasting a lot of time dealing with trying to reproduce a [27] that I don't think existed, and then it was scary for a couple minutes because I even messed up reproducing the [29] I thought I had secured, but that was realtively easy to resolve since I think I just made a misturn and was pretty confident it worked because I checked it earlier.

I'm also kind of stupid because I should have just looked for a shorter way to just get to {3c}, and in going back, sure enough I found:
3-2: L' [D' R' D R] L; i.e., +[5] {3e/2'2'c} -> {3c} [22], and then within this I found
3-2-3: L2 D R D' L2 D R' D'; i.e., +[4] -> {}

Not even sure that's the best option, but it's pretty decent.