Except that it's hard to keep the screw from turning if the head is buried under putty & an overlay. Sasquatch! nailed it, t-nuts are the correct way to do this for a clean layout.
This is great stuff, I didn't mean to imply there was only 3 ways, I was just suggesting 3 common ways. Most people don't know what a t-nut is.
Use carriage bolts, they shouldn't turn. If they do your kind of stuck but they shouldn't as long as you don't go crazy tightening them.
I agree t-nuts would be better but you still need to fill and sand unless your using some kind of hard overlay. There are threaded inserts that can go in from the bottom, then you don't drill the hole all the way through and you could remove and relocate them if you replaced the joystick with a different bolt pattern. Its just another option but for maximum strength you should go all the way through the panel and use t-nuts or carriage bolts.