I found an online manual saying that this tool grinder uses both a left and right-hand 5/8-12 Acme* nut, which is confusing. Since the grinder runs in both directions, one wheel will always be trying to loosen its nut, so I wonder if they decided, "better to have one always wrong rather than both wrong in one direction." I'd have made both correct in the normal forward direction, but what do I know!
I can either try to find a nut, or buy a tiny boring bar, and make my own HSS cutter. The trouble is that I'm very new to both threading and using the tool grinder for its intended purpose, but I guess that's how we learn!
* I was wrong, see posts below