Thanks for all of the advice guys! It is actually a factory metal panel that uses carriage bolts. And I haven't put the overlay in place yet. I'll try and see how far I can countersink the flat head machine screws, unfortunately the control panel is pretty thin (1/8" or less i'd say), so i'm not too hopeful.
I was hoping maybe there was some hardware or something you could get to do this, so that the joystick attached like the buttons do...oh well. By the way, I haven't actually picked up the Happ supers yet, and noticed on all the joysticks there's a circular disc that goes on top of the control panel. What is that? A sticker? How does it attach?
Thanks again for all the help!