TDM
Legend
I find this method to be fastest, especially if you use Roux:CF sounds like it would be pretty hard, but I'll give it a shot.
1- Corners like 2x2, 5 seconds
2- Fix two centres (Rouxblock colours), <one second
3- Three edges on L to make a Roux (preserving corners), ~6 seconds
4- Three edges on R, leaving just LSE, ~5 seconds because easier lookahead
5- LSE, ~3 seconds
Total = 20