Lt-UnReaL
Veteran
As I was solving today, I was on the 4th slot for F2L, and as I was about to do U' F' U F to put the CE pair in, I realized that the ENTIRE cube was oriented and permuted, except the 2 cubies in the slot, and the 2 cubies that made up the connected pair. So then I just turned it to the side and did the J perm.
It would have been an incredibly fast time if I had timed myself. 
Do R2 B R B' R D2 L' F L D2 with cross face on the bottom to see what I mean.
Do R2 B R B' R D2 L' F L D2 with cross face on the bottom to see what I mean.