I finally got the chance to trim the flange off of the 18" dome that I got from Barnards in Chicago. I used the flush-cut attachment on my Dremel MultiMax and it made a nice even cut around the flange. There were some plastic goobers from cutting stuck to the dome edge, but they came away easily.
I was going to mount it to a 1/2" plywood dome ring, but the motor burnt out on my Dremel rotary tool. I'll have to finish that up later with a jig saw.