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Tiny Screwdriver!
My buddy dBm took pity on my plight:

Tiny screwdriver The far end has a 2.5 mm hex driver, although I’ve never encountered a nut for an M1×0.25 screw in the wild. It doesn’t fit an 0-80 nut and gulps 00-90 nuts, so it’s definitely hard metric.
My collection of glasses required an aggregate two turns of tightening, which prompted dBm to remind me of threadlock.
Done!
Thank you, dBm!