I'd also attempt to reinforce the joint. Perhaps a pin vice and a micro drill bit to drill a few mm into each face of the break, then a piece of wire to bridge the joint.
^ This.
Absolutely.
You are going to need number drills, as opposed to those measured in millimetres or decimal point sizes thereof.
They are thinner than a thin thing - a model shop or watchmaker supplier could be your most effective source for these.
And piano wire.
If you are able to make more than one pin joint, so much the better.
With a steady hand, you should be able to make more than one hole on that area where it has fractured.
Don't worry too much that the holes on opposite sides of the fracture don't line up perfectly.
Do the best you can, and rely on rubbing down the excess adhesive to get a decent looking joint.
It's highly likely that the frames are acrylic - in which case any cyanoacrylate adhesive will do.
Personally, I'd go for one of the thicker ones as these have gap-filling properties although they are slower to cure.
You could use an accelerator but, as with most things, you don't get something for nothing - an accelerated bond is usually weaker than one which hasn't been accelerated.
FWIW I've used the above method to successfully repair broken mould formers with a wall thickness of 3mm or less on a number of occasions.
ETA - Oh, and I'd steer clear of Dichloromethane - it is a known carcinogen - I'm still trying to figure out what to do with the half litre of the stuff I have in the cupboard under my stairs - But it looks like you have this covered upthread.