[Sébastien]

did you try doing this after your 2x2x2?
(B U' F' L F U L) // 2c2e

i know 13 to 2c2e likely won't give better than 21 but it's still an option

Interesting! No, I did not see this, but I would have definitely tried the L3C first anyways.

I just looked at the skeleton but did not find any really good insertion. The best I could find:

L' * U' F' L' F U B' R F' U' R2 F L2 #

* = D (D B' U' B D' B' D B' U B D' B2 U' B2 U) D' (V-Perm)
# = L (U R B R2 U R U' R B' R' U' B) L' (ZBLL)

giving 27/26 moves.