It's been a while so maybe I'm misremembering, but can't you solve a 4x4x4 by reducing it to a 3x3x3 and solving that? Pretty sure that's how I used to do it. Treat each 4 as a 3 with a fat middle: 1-2-1. Then solve the centers (2x2) and the edges (2x1) with standard moves and you've got, essentially, a 3x3x3.