I made a new 4x4 direct solving method that is directed toward CFOP users. I got a 1:36 ao5 with it, and I average 1:17 with Hoya.
Step 1: Cross and centers
You can do this with Yau or Hoya, whichever you prefer.
Step 2: F3L
What you do is use F2L techniques to solve a corner and a wing, then solve the other wing using keyhole. If you cannot find the other wing, you can start solving another slot until you find it. For the last pair, you use a commutator to solve the last wing. Match it up with its center, hide it on the bottom layer using a slice move, do a sledgehammer, slice back up, and insert the pair.
EDIT: You can also insert a single wing, move it out of the way using a Uw of d move, and solve the rest of the slot using F2L techniques.
Step 3: CLL
You can use whatever OLLCP algs you want for this. The only things that matters is that you preserve the F3L and solve the last layer corners.
Step 4: ELL
You have to use commutators for this. A great way to do this is to solve 2 opposite edges, then solve the last 2 dedges with one algorithm (they can be found on the KBCM wiki page). Since I am not very good at 4x4 ELL, I solve one wing at a time using 2 simple commutators. When the top layer sticker is facing up, I do F R' F' r' F R F r. When the top layer sticker is facing to the side, I do x' r B' R B r' B' R' B. There are also cases that use flipping algs as insertions.