I cut out the top holoprojector hole in the inner dome tonight. At first I tried using a hole cutter for a drill press (twisting by hand that is, no drill), but I could see that was going to take forever. So next I turned to the brute-force method, using a drill (11/64" bit) to cut small holes around the circumference of the hole.
I'd classify this somewhere between "butcher" and "massacre." I'll come back with the Dremel later and try to smooth this out. I've already started, but obviously there's a long way to go. It appears to have had a happy ending, complete with cutout on top for a crown.