Well, I started by making these pickup covers:
They turned out pretty well, if I do say so myself.
After that, I thought the pickup rings would be easy. The first one I tried to make was with really thin Brazilian rosewood scrap. I cut out the inside just like you did, but didn't do a template. I kept breaking it and gluing it back together. Finally, I moved to some cocobolo that was lying around. This time I just cut off all the edges with the intention of gluing them back together. But I goofed up, and one of the sides was too short. It's not a hard fix, but these have proven to be a little more difficult than I anticipated. I think I'm gonna go with your method, except I'll probably route with a Dremel. Incidentally, I've been using a coping saw for most of the work. As long as you're patient, it seems to be a pretty decent tool for the job.
Thanks for the replies. NotYou, make sure you let me know how it goes. I'll do the same.
-Dave