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35, 28, 28 = 30.33 mo3 PR . Tied @Cale S on the last two!!!!!!!

Solve 1 was 20 to 4-twist, I inserted double hedge for 26 to 3E. Had 1 minute left so I just stuck U2 R U D' F2 U' D R U2 at the start.

Scramble 2: R' U' F U2 B2 U2 F2 L2 U2 R' F' D L B2 L D' L2 U' R' B' U2 R' U' F

Spoiler

D B // EO (2/2)
L2 U L2 // 123 (3/5)
D R U F2 D U' R U F2 D // 5C (10/15)

D B % L2 U L2 D ^ R U F2 D U' R U F2 D // 5C (15)
%: B2 L' U L B2 L' U' L // 3C (8-2/21)
^: D2 B U B' D2 B U' B' // (8-1/28, IF says 27 is optimal)

Final: D B' L' F L B2 L' F' L' U L2 D' B U B' D2 B U' B' R U F2 D U' R U F2 D (28)

Scramble 3: R' U' F D' U' F2 D' B2 D' R2 U2 L2 R2 F R U' B' L' B D2 B2 R2 D2 R' U' F

Spoiler

(L U' F R') // EO (4/4)
D' B' F D' // 222 (4/8)
U B U2 (U) // 223 (4/12)
(B2 U B U' L2) // 5C (5/17)

D' B' F & D' U B U2 L2 U B' U' B2 U' R F' U L' // 5C (17)
&: F U2 * F' D' F U2 F' D // 3C (8-3/22)
*: L2 F' R' F L2 F' R F // (8-2/28, IF says it's optimal)

Final: D' B' F2 U2 L2 F' R' F L2 F' R D' F U2 F' U B U2 L2 U B' U' B2 U' R F' U L' (28)

What is that first insertion? I've never seen something like that before. I guess a better question is if this is something intuitive that I just need to think about more or is it some set alg that you have down for this very occasion?

What is that first insertion? I've never seen something like that before. I guess a better question is if this is something intuitive that I just need to think about more or is it some set alg that you have down for this very occasion?

If you use Rniss at that point, the cube is an F2L-1. That insert is the optimal alg to solve the F2L pair which I learnt a while back. I saw it this way, although the setup to sexy way of viewing it is valid too, but perhaps less obvious to find

Not really an answer, but I once wrote a NISS block solver and I think it managed to solve a fixed 2×2×2 block (i.e. not colour neutral) in at most 5 moves >90% of the time. (Let me check again; don't quote me on this yet.)

And yes, knowing three of those will give the fourth.

E: Ran 40 solves (fixed block, as mentioned above).
4 moves: 8
5 moves: 21
6 moves: 11
So ">90%" was an exaggeration. For CN block, this seems to suggest that it's almost always possible to do it in at most 5 moves, 4 if you're somewhat lucky. Without NISS/premoves, this is the distribution.

Cologne Open 2018, Scramble 2 -- Best result on this at the comp was 28 (?)

R' U' F R2 B D2 U2 B D2 L2 B2 R2 F' D' L' F R' B2 L R2 F D R' U' F

24

B' // 2 pairs [1/1]
F' D' // sq + 3 pairs [2/3]
(B2 R) // sq + 123 [2/5]
(F D2 F2) // 222 + 123 [3/8]
B' U' (U) // F2L-1 [3/11]
(L' B' L' B) // F2L [4/15]
(B' U' L' U L B L2) // 3c [7-2/20]

Skeleton: B' F' D' B' U' L2 B' L' U' L U L B L U' F2 D2 F' ^ R' B2

^ - F2 R' B' R F2 R' B R [8-4/24]

Solution: B' F' D' B' U' L2 B' L' U' L U L B L U' F2 D2 F R' B' R F2 R' B' (24)