Some of these are at least silver plated. But has anyone ever melted just a pile of movements and had it assayed?
Not talking cases, this was just a small pile of movements I have from a watchmakers estate. Nothing valuable in terms of watch movements.
As an example, I can see that the balance wheel on some of these appears to be either a heavy gold plate, or possibly karat for it's density.
You probably has them as mixed lot, so separating and assaying single pieces does not have benefits for you. I regularly do XRF "assays" like this:
1. weigh the starting material
2. melt to form uniform button
3. hammer button flat and sand off the surface to show fresh metal
4. weigh the button to assign the melting loss
5. shot the sanded flattened button with XRF, which determine PM %
6. do the math
Not superextra accurate, but if the XRF machine is from upper-middle class, error is within 5%. Measuring solid metal samples is relatively bulletproof, and you can happily round the PM content to the grams per kg. Less than 1g/kg is somewhat troublesome with bigger error margin, but from 2g/kg higher it is everything I need when buying scrap.
I would advise to melt the stuff to one button, sand it nicely with sandpaper or angle grinder and let it zapped by someone. Quick and very informative. I regularly do micro-assays of pins, plated boards, contact points and MLCCs etc by this technique.