I don't see why that wouldn't work. Just have a metal shop cut out a rectangular sheet of metal with the holes drilled in the right place, and you can just bolt that to the frame of the wood structure that you are building for the other panels.
Another option would be to have the metal shop construct mounting plates, much like a trackball mounting plate that you can recess with a router so that it does not show. The plate would have threads tacked on to the bottom so that you can screw it from the underside of the panel, then just bondo away on the top to make sure it's smooth after you recess it and stick the overlay on the top.
A third idea would be to route the underside of the wood control panel enough so that you have good clearance on the stick. On my current fighter layout, I have 2 Wico P360's mounted and I had to recess a good half an inch until I got the height I needed on the sticks. The MDF is still plenty strong, so no worries there, just make sure that you go slowly recessing such a big depth.