I have a drive belt for the Burgmaster that works! The tooth pitch isn't quite right, but no one makes the original anymore and this seems to be as close as you can get with a modern, stock belt. I suspect it will be absolutely fine, particularly since this isn't going into production use or anything.
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And look at it go!
Don't forget, that's entirely mechanical! A little button gets pushed at the top of the stroke, which initiates a fascinating sequence of actions: stopping the current spindle, retracting a little nub that locks the heads into a specific position, rotating the head 60 degrees via a geneva wheel, pushing the nub back out to re-lock it, and finally starting up the spindle that is now facing down. Marvelous!