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Hi, David Cannon. Heh, I've actually cheated a bit - most of my original
higher-D thinking was done about 4D. Later, I applied those ideas to 3D. 

I have a distinct philosophy about higher-D games, and that is to let the
board star. It came out of my decades-long struggle to design a good,
playable 4D game. I learned [the hard way, which is apparently the only way
to learn - for me, anyhow] to not clutter up the board with pieces, and
also that even regular pieces do tricks in higher-D. You don't really need
complex pieces to enjoy the thrills of higher dimensions. David Paulowich
quotes something from the beginning of this thread about chaos. I believe
too many pieces, with too many different moves, lead to chaos in a game.
But that outcome is certainly not inevitable, especially in a 3D game.

I think we are misled by the starting piece densities in the 3 main forms
of chess. Very few people realize just how small the boards are in these
three games. Instead of thinking 50% is the perfect number, turn it around
and look at what else FIDE chess could be. In simplest terms, could you add
another row of pieces to each side? Could you take a row away from each
side? The 8x8 board has certain limitations inherent in its small size. 
Now look at the Eastern games. With bigger boards, they drop piece density.
They could ramp up densities to the 60% or more level, but don't. Instead,
with larger play area, both games thin out the pieces. Admittedly, people
don't tend to look at it that way, but people don't intuit statistics
well. 

Clearly I have a minority opinion. But I like opinions much much better
when they have solid facts as their base. The only real way to get any
facts is to run tests. And pushing pieces often helps clarify design
issues. So I'd like a show of hands on keyboards: who is interested in
participating in a 3D [and maybe 4D, if wanted] group playtest session?
Even if only to watch and maybe kibbitz.