I solved it after about 10 hours. The very tricky part, as I mentioned
in my last message, is to move the edges about in a plane. I still do
not have a move which moves 3 in one slice (nicely), rather 2 in one slice
and one in the adjacent slice. This makes the process very time consuming.
I also believe centers first is probably the way to approach it although
it is just a feeling. I think that moving only some of the center cubies
will require very complicated transformations.

I would guess this cube requires about 10 times more moves than C^3.
Does anyone else care to speculate? I will be surprised if anyone
will ever solve C^4 regularly in under 10 minutes.

Two questions:
1) Any comments about cube-lube. This cube is massive and needs some.
2) I heard there are about 10^50 configurations, true?