I don't think you'll be very happy with bottom mounting that joystick, no matter how close you try to raise it up.
You'd be better off cutting your hole for the joystick trunk, and then use a router to create an inlay in the shape of the skirt. Yes, the top surface (under the dust washer) of the joystick is not flat, but you could easily fill that in with a filler of your choice -- bondo, etc. Or you could just take it apart, and sand the top of it flat.
If the stick is going on a wood control panel, chances are you'll have an overlay and then plexi over it, so you shouldn't need to worry too much about the surface strength of the putty. If you sand it flush, then no worries.
A 3rd option would be to make a metal mounting plate for the stick. Flush mount the plate, weld nuts to the underside of it (or bolts) and attach as necessary.
Just my $.02 worth *plink plink*