My first question is whether this is a "collector quality" piece, or whether it's beat up and you are just trying to get it working to give to the kids to play with?
If the latter, I'd be really tempted to hack in some low-profile PCB-mounted miniature switches. Might even be able to drill a hole in the pcb for the actuators and bottom mount them.
But if it's in collector condition, I'd look for the parts.