Is there some sort of adapter that will allow this joystick to be used in place of a standard joystick? (The longer side seems about right, but the shorter side is too short).
Also, what is the thickness of the base? (For months I've been searching for a joystick with a shallow profile and long stick for a wooden CP that has very little space beneath it).
The item you linked to
does not function as a true 4-way. You will likely be disappointed with the ease in which you can hit diagonals with it, even in it's supposed 4-way mode.
As for mounting, just rotate the stick 90 degrees and it will fit between your current mounting holes.
Simple geometry indicates that longer sticks sometimes make for sloppier controls. If you like the tight reaction time of the old school 4-way controls, you pretty much need to route a pocket into the underside of your panel. Either that, or flush-mount them, which will take care of your depth concerns as well.
RandyT