My J-Stiks are mounted under 5/8" (15mm) MDF atm, with no routing. They feel much too short for me, when I make my final panel I'm probably going to use a metal mounting plate. Alternatively I'd route the MDF down to ~5mm.
Edit: on the restrictor subject, I presume the octagonal ones would make a J-Stik lose it's 4/8-way switchability. Just a thought if you want to play 4-way games too.