How to remove..

Real men use their teeth when all else fails.

I guess hammering a larger bit in is out of the question with it being an xb360. I think you're snookered unless you go down the drilling the head off route. You'll just have to make sure there are no filing on the pcb when putting it back together.
 
When you say "drill it out" how do you mean?

Get a slow, low powered drill (dremel on sloooow mode), a drill bit that's smaller than the screw's body, place drill bit on the screw (where you would usually be screwing), and then slowly drill into it. The drill bit will (if you keep it straight) drill down into the screw body and help it turn right out.
 
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