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David, you've posted a radical 3D variant here. I'd love to see how it
plays. Why radical? Because the pawns do not fill the 'pawn level' [as
the pieces do not extend to the edges of the 'piece level'], allowing
pieces to sidestep and bypass all the pawns. This ought to change the
opening dynamics quite a bit. 
You commented in another post [Play this Game!? 6/6/07]:
'But after 100 years have passed, I would expect the Raumschach page to
have a brief outline of how to force mate with King and three Rooks. Or is
it four Rooks? Who is actually playing 3D chess variants nowadays? Does
anyone still read Jim Aikin's page on the 4x4x4x4 game Chesseract?'
The key problem in 3D and higher-dimensional chess variants is how to mate
the king. The Yahoo CV group had quite an extensive discussion of this
problem, with various solutions proposed which can be explained briefly
here in a later post. The usual method is to restrict the king in some
manner.
On 4D chess, my understanding is that Chesseract had some popularity as a
Zillions game. The 'slippery king' problem is magnified in 4D. I've
[independently] designed a couple of 4D variants, and I admit to having
considerable difficulty in reading and understanding Mr. Aikin's post.