The router was my friend on this one. See how I mounted my 2.25" E-Ice trackball.
Results on page three. Hope that helps.
-csa
Totally sick.... and exactly the sort of thing I was looking for! Do you think the same method will work with a 3" Happs High-Lip? I am also worried about the 1/8" remaining material being too thin. How is it holding up? Thanks!!! 
It's holding up pretty well, considering I haven't played on it yet

I haven't hooked it up in all it's full glory.. Artwork arrives at the end of the month.. trying to finish it fully before plugging in and never looking back.. that's for another thread.
But I don't see it being an issue honestly. Those three screws hold the case in super secure, and you really aren't putting weight on the thin piece carved out. The top of the plastic shell rests snugly on the bottom of the thin piece, and the screws are doing all the supporting. I'd assume my technique would also work for a 3". You'll obviously need to change measurements.
Also, if you are using mine as a guide, do note which way is *UP* on your trackball before mounting (metal vertical roller at bottom of screen, metal horizontal roller on right). I cut the hole out upside down, then had to do some hacking.. where I finally ended up with a roller at the top and a roller at the left. I'm not making that control panel a 3rd time

Hit me up if you have questions about any of that.
-csa