I've veneered over 3/4 birch ply with no problems. *The substrate
is stable and it doesn't seem to make any difference whether the
veneer is parallel or cross grain to the top layer of the ply. *The
edge is a different story as the internal layers can telegraph thru the
typical thin veneer. *Wrapping the edges with solid wood first solves
that. *I don't bother veneering both sides of 3/4 ply and have had no
issues with warping.

Alternatively you could use MDF for the substrate. *It's very flat and
usually less expensive than bitch ply. *If you already have the ply that's
a different matter.
Art

Perfect. I'll have to keep an eye on the edges -- definitely not
something I would've thought about until too late. I plan to do an
ebony stain on it, will that help or make it worse? MDF would
definitely be perfect, but I hate working with it. Last time I made a
subwoofer cab with it, every crevice in my garage was covered in fine
dust. Plus something about using real wood makes me feel better about
quality, even if layered.