I just lost a long reply, so this one will be brief.
The best way to do it is vacuum veneering. See
www.joewoodworker.com for all the supplies and info you need.
Your method will work, I've done it myself. Use veneer glue, like joewoodworker sells, or Titebond cold press veneer glue (available at Rockler if you have one near you). You'll be limited to 8-10 inches wide, and use a lot of clamps. Every 8-12" on each side of the board.
The water based gel stain shouldn't be a problem. I use water soluble dies, which is the same as pouring water on the finished panels, with no ill effects. I've run into problems with water based polyurethane topcoats, though. If the veneer is loose anywhere, water based topcoats can cause bubbles, due to the slow drying time.
If you have any more specific questions, just ask.