The spindle is an ISEL UFM500 universal spindle:
https://www.isel.com/en/universal-mi...e-ufm-500.html
Sadly the website doesn't give any hints on which tool to use to unfasten the nut.
I've tried ordering the spanner Dave suggested from McMaster, but they refuse to sell it to me because of "the cost of complying with U.S. export regulations" whatever that means. However, now that I have a pretty good idea of what the tool looks like, I'm going to try milling one myself using the cutter that's already in the spindle (and hope it doesn't break!).