My advice is you should do the full Yau method.I'm averaging ~2:15 on 4x4 with a weird Yau-Redux combo. I do Centers->White Cross(edge pairing)->3-2-3->3x3 Stage. I do that because It's like 30 sec faster than me just doing normal Yau, although I don't have much practice with yau. What should I be practicing to improve? Also, my 3x3 average(3x3 puzzle, not 3x3 stage) is ~20 seconds.
3 white cross on the left side
Last 4 centers
Last white cross
Your time will get worse at first, especially in the part of the 3 white cross, but over time, it will be very fast.
Is that not even when you switch from layer method to F2L at 3x3, at first your times will get worse, but with a lot of practice, your time will be so fast.
I can't do the last white cross on the left side, i need to rotate, but i will practice soon.
This is my experience, I'm new at 4x4, but practicing for 2 months and I my avarage is 1:15~1:20