Well, i'll tell you my experience.
I have a 3/4 " plywood top panel and i routed out a 2/8" amount of wood from the underside of the panel to allow for my joysticks to be up high enough.
I ended up useing a black and decker rotary saw which i could set how deep it would cut and it worked great!
Ild say if you haven't put your panel together yet (ie: the sides and bottom) then use a router to cut your depth. it seems like you will need to cut out about 3/8'ths deep to get a good joystick throw.
i also ended up useing an 1 3/4 inch hole saw for the hole for the joystick. It worked great!
Might want to get a second oppinion on how deep to recess the routing to allow for the lexan as i didnt use any lexan. I found some good enamel paint works just as good.

Lesscutting too hehehe.