Has anyone tried to match a scrambled 4x4x4 cube? It's been a fun challenge that requires learning supercube-safe algs (especially for PLL), and I can succeed 99% of the time. Roughly 50% of the time, though, I have to swap two corners on the last face. There are no supercube-safe algs that can do this, however. You can find t- and j-perms that work great, but rotate the top face 90 degrees. Then if you rotate back and fix the corners and edges, you end up with a completely matched cube except for a 90 degree rotation on the top face (see below--trust me, the rest of the faces match exactly). I know it is impossible to rotate a single face 90 degrees without affecting another part of the cube.
I found a parity alg that swaps two corners and only two adjacent center pieces, so if there is a bar on the upper face, this alg can be used to match the given cube. The bottom line is that whenever there is a bar on one of the centers of the initial scrambled cube (which happens almost every time), I'm just sure to set up my match so that this center ends up on the top face at the end. But what if the initial cube has no bars in any of the centers and I'm left with this last-two-corners parity?
Any advice would be appreciated!