Final(?) update: I was able to resolve the nightmare bat problem by upgrading my Android build tools from 33.0.1 to 34.0.0-rc2. The problem just disappeared. Terrifying.
After a full workday of fiddling I am now able to build APKs on Windows as long as I invoke the build three times, after each of the first two unsuccessful builds manually copying a file that CMake put in the wrong place. This is one of those successes that makes you just feel more defeated than if you'd lost