I am grateful for your prompt, thorough, helpful response.
And the answer is ... #4: don't launch the .air from a network drive. I've been caught by that before, I remember now, though it's been years since I needed an install or reinstall. And usually I'm pretty good at seeing past incorrect error messages.
It's good to have 1.5.1.2 in any case. I can't find any reference to it past the checksums you linked -- any user-visible changes from 1.5.1?