I do know how to switch zones - I follow the instruction manual. ; )
This morning I removed the thermostat from the wall and removed the board from the housing. The switches are in a neat little line and they are assembled with little clips on the sides. I gently opened the clips and removed the moving button for each switch and cleaned the contacts with contact cleaner. The contacts looked nice and even - none appeared bent or broken. I reassembled and things seem to work properly (at least for now). I press the top two buttons and in a second or so, the zone changes.
Warning! The parts are small, the spring is springy, and the contacts will shoot out of the switch when you shoot cleaner into the switch. If you are not steady, or have big fingers, or have poor eyesight, you might just lose important parts. (disclosure: I am marginal in these respects, but very adventurous! I also found the tiny spring and contact on the garage floor.)
The sure thing would be to get with one of the ebay thermostat rebuilders or just go to the five-button system. If you are of the type that thinks "Well you can't make it more broken," dig in.
Wish me luck!