In the end I tracked down another Watson "Standard Metallurgical"
microscope on eBay. It's in better condition, but still has a few
issues. With spare parts from the first I should now be able to build a
microscope in good working order.

For the benefit of anyone who comes across this thread in the future,
the reflector in the Watson "Standard Metallurgical" is plain glass, not
a semi-silvered mirror.

Many thanks,

Chris