I think I'd stick to either cherry or mahogany, Brad, due to the tight grain, stability, and ease of working. Even white oak has fairly large pores, and would require meticulous filling and sanding at the unassembled parts stage to avoid having hiding places for grit and dirt once assembled. Accent pieces made of more exotic woods might also be interesting.
One important consideration is finding kiln-dried woods, so you'll know the pieces are already reasonably stable. Even with kiln-dried wood, you'll encounter situations where internal stresses aren't disclosed until cut into smaller parts. The larger DIY chain stores are less likely to be concerned about selling only quality, kiln-dried materials.
Being as you're in Pleasanton, you might be interested in a trip to Southern Lumber in San Jose (on South First St. at the south end of downtown). They have an excellent selection of both conventional hardwoods and more exotic woods, too. Plus, they usually have scrap bins of smaller pieces of the exotic woods that you can dig through. I believe there is also a hardwood supplier in Berkeley or Alameda that caters to furniture makers, and might be worth exploring.
If you're OK with the idea of a hybrid, you might consider finding a used Toyo back. It's a two-piece design with a mounting frame that would be easy to adapt, and which provides a Graflok interface, and the Graflok-based GG portion. That's the approach I took when making a reducing back for my 8x10 Tachihara, allowing me to side-step the issue of finding special hardware. All I had to do was make an adapter frame that used a combination half-lap/miter joint for the corners to avoid light leaks.
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