I made some progress.
Couldn't find the M500 service manual to save my life but the M700 seems to be it's big brother.
https://archive.org/details/manual_MULTISYNCM700_SM_NEC Would still like to find the M500 service manual if it exists.
Recapped the whole board without success. But the capacitor list for the M500 I made myself is close to identical to the M700, I think about 20~25% might be different. And a lot of other parts are also the same.
Also followed the circuit and shorted Q2006 Base and emitter, which resets the latch: C5G3 rises to ~58 V, HV comes up, and after a few seconds I get a normal picture. If I hold the short until the picture appears and then remove it, the monitor keeps running normally. The latch only trips at start-up. A hot restart (off 2-3 s, then on) also trips, so it isn't a cold-CRT / no-beam-load issue.
So something is tripping the latch on startup. Don't know what yet.