So after a lot of messing around, I have established that the problem is caused by the driver for my graphics card. The card is old enough that AMD no longer supports it, and neither version of the driver I can download from AMD's website works, so I'm going to guess there is some incompatibility between that version and this Insider Preview release.
I will try a newer build (I was going to stick to the Slow ring, but if the current Slow build is broken I might as well go Fast), but if that still doesn't work I'll reinstall plain old Windows 10.