Experimental Methods

I happen to know all 2GLLs. :D

Is there somewhere I can happen to find the permutation algs for the corners?

http://www.speedsolving.com/forum/showthread.php?t=8871

This was originally a thread for ZZ-d, which permutes 6 corners while solving the LHB in ZZ, but changed to permuting 4 corners while solving the last slot. It assumes you are using a method that orients edges in a previous step.
 
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Here is an example solve of that in-between method I mentioned above.

F2L minus 1 slot = 16 moves
Orient Edges + Solve slot edge = 7 moves
Solve F2L corners + Permute LL Corners = 13 moves
2GLL = 16 moves

52 moves

Method averages about 50 moves and uses about 50 algs. I think it's pretty neat... There are no difficult recognition problems like with the first method I proposed.

Solve from above ^:
http://tinyurl.com/algB-U-D-L-RF2U
 
I've actually been developing this method with another member of the community (joey), and it looks very promising.

Here is an example solve using the current list of algs:
http://tinyurl.com/algF2R2D-FDLFUR

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

2x2x2: F2 R2 D' F D L
2x2x3: F U R2 F2 U' R' F
F2L-Slot: U F R2 F2 U F R2
ELS: R U' R2 F R F' U'
CPLS: U R U R' U2 R U R' U
2GLL: R U R2 U' R' U' R U R U R2 U2 R' U2

This was an entirely average solve. Every single step was literally the exact average movecount or 1 move away from it. The total solve was 50 moves (But only 47 if you combine the R2 R' and cancel out the U' U I did between algorithms. I like to think that this solve was 49 moves because I did R2 R' fluidly as one move but the U' U was clearly not fluid. So, 49 move solve). My quicker-cubing-comrade (joey) is already sub-20 with a basic form of the method (F2L - 1 slot, intuitive ELS, he just learned some of the CPLS algs yesterday, and is using 2-look 2GLL). With that knowledge I'm confident that this method in full could match Fridrich/MGLS/etc..
 
So, here is my idea - you solve F2L normally, then EO combined with CP -> 2GLL. Should be good for OH solving, because EO + CP algs are pretty short.
scramble : D R' F' L D F' B D L B R' U2 R F2 B2 R2 L B' L B F U2 D' B2 R'
solution :
x2 y' R2 F2 U L F'
U' L U' L' U2 y R U' R'
U' y R U' R'
R' U R U2 R' U R
y R' U' R U2 R' U' R U R' U' R
F' L F L' U2 L' U2 L
R U R' U R' U2 R2 U R2 U R2 U' R' U
56 moves total
 
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