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...