Wonderful pince nez sir. I have a similar pair, except mine have smoked lenses. Mine too are fairly loose and fall off after a few minutes when I try wearing them and walking at the same time!
But I'm loath to do anything that may damage them.
(Actually, it's "Miss", but no worries; I realize the avatar is misleading

).
I found your thread, and that is a lovely pair! I'd like to find a shaded pair as well. I had originally bought these to use as a prop, but realized they aren't prescription lenses, but low-magnification reading glasses.
I agree, I wouldn't advise attempting anything that might damage them. I considered purchasing some spirit gum and simply glueing them to my face when I wanted to wear them, but curiosity got the better of me today, and I took them apart (!) :

I couldn't remember where I'd left my micro-screwdriver and had to use the wee dental chisel on the left to unscrew the screws.
I took the opportunity to finish cleaning up all the separate pieces. Bending the bridge was no easy task--it's a really strong piece of metal. It's important that the "kink" on either side, above the screw holes, not take on too acute of an angle, so that the lenses are brought closer together when they're reassembled:

Voila! Pinchier Pince-Nez!
They stay on great. I've been wearing them all evening. I'm wearing them now.
Looking at the photos of yours, James, I wonder if you couldn't adjust them by just sliding the top ring--where the bridge passes through, on either lens--farther up the bridge? Maybe that would bring the nosepieces closer together, without having to bend the bridge at all.