Briggs2 (B2) (3x3x3 CP method)

If we use the followup to CPFB (which can be done in ~10 STM)

SBsq (~7)
pair (...4?)
CLL + 4flip (10, going to go with shadowslice's stat here)
LSE (11, seems like a reasonable enough estimate as long as the 4flip you're forcing is either arrow or M2arrow)

= 42 STM

Could be pretty good. I'm a little bit worried about CLL+4flip recognition but maybe that will sort of be like OLL recog with time since you are just looking at U/D stickers. The movecount is nice and lookahead decent given that it's basically advanced Roux.

EDIT: Oh right, two other things: first, inspection is obviously hard but the CP is planned entirely in there, so there is no pause to do that stuff. Second, in order to get 10 STM CPFBs you will have to be fully CN. I think this is kind of neat, others may hate it, idk. Figured that's noteworthy.

EDIT: Also the pair making could take more than just 4 moves if you get a really ugly case. Hence why I wonder if it's better to go with: CPFB (10), SBsq (7), CLL + last corner (10), L7E. Don't know how much L7E can be optimized but my intuitive sense is that this might be more efficient, depending
 
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BLS algs improved with insertion and OLLCP:

M0xxx-(U) R U2 M' U R' U R U2 r2 U' R U' R' U2 r
(U') R' F R F' U' L' U' L U L F' L2 U' L U F

M1bxx-(U') R' F R F' r' U2 R2 D R' U R D' R2 U r
(U') R' F R F' R U R' U' R' F R2 U' R' U R U R' F'

Hopefully you get the picture. I took the case, inserted with R U' R', R U2 R', and R' F R F', and did the resulting OLLCP case. Usually, one of the three will yield a nice alg.
 
Hey, sorry for the thread bump but I really want to learn this method just for fun but can't for the life of me figure out what you meant in the explanation of the CP part. Could you help out?
 
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