And we members of your fan club can’t wait to see the results. 
Just thought I’d give an update. Using the diamond wheel with a sponge to keep the glass under water works pretty durned well. (Makes a helluva mess, though. The wheel throws off a whole lot more water than the drill bit does.)
Dropping frozen glass pieces into boiling water didn’t make them break, but I’m going to try freezing them then pouring boiling water over them while using a wooden spoon handle or something to put some pressure on the saw cut. Since the pieces are slightly curved, I think this might work.
Using the wheel to score the glass and pliers to snap it along the score line, I was able to produce pieces about an inch across, which is exactly what I was after.
Thanks, all, for your suggestions!
Not much of a temperature difference there. Do it the other way: heat it in the oven to, say, 450 (5-10 minutes should be enough) or so then drop it into ice water immediately.
I will try this!