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Wow, in the time it took me to actually answer Mark, Gary and David have
gone past my comments. One of the thrills of being more or less a Mr. Mom
is the incessant distractions. Let's see if I can get this one done
before 6 more people supersede me.

Gary, I think you picked pieces that people like because they add a very
simple move to a power piece to make it even more powerful. Apparently
chessplayers, like soldiers, always want a little more firepower. These
pieces are easy to understand and very natural for chessplayers to use.
I've been thinking along your lines for a couple weeks, and I am
interested in looking at similar changes, but with a shortrange twist [of
course]. I've been considering replacing the rook and the bishop, but
with shorter ranged pieces that gain a leaping ability. I'd cut the range
of the R and B down to 4 squares. Then I'd add the alfil move, the 2
square diagonal jump, to the rook's move, and the dabbaba move, the 2
square orthogonal jump, to the bishop's move. All else as it is in FIDE
[now and forever, amen???], but the rook is an AR4 [sounds like a weapon]
in Betza notation, and the bishop is a B4D. These pieces are not quite as
intuitive as yours, and the queen piece is more problematical. On a larger
board, I'd probably make the Q the combo new piece, a Q4AD. On an 8x8,
I'm less inclined to let the queen jump. And this is running long - more
later