You have a couple of choices. I just finished mounting a CMoy in a block of hollowed-out red oak. My sides were almost half an inch think.
I used both of the following solutions for different panel components.
First, for power switch and volume pot, I used a dremel rotary tool with a tiny drum sander to grind a concave section on the back side of the wall. You are probably pretty close to being able to get a 1/8 jack (standard depth) into 2mm plastic. If you can grind just enough away from the back to get one good turn on your retaining nut, that'll do it. Don't skip the washer, tho. It'll scratch your faceplate.
Option 2, which I used for my in/out jacks, was deciding to go the 1/4" route for both, as in doobooloo's recent gorgeous wood META. Switchcraft makes a beautiful deeeeeep 1/4" jack that is carried by both mouser and digikey.
Of course you have to use adapters on your cords, or, like me, whip up some 1/8->1/4 IC's.
GnD