Thanks to those who tried to help, I got it working just now, after spending an entire day on it.

I'm not sure what exactly the problem was. After reinstalling VS, VS installer, SDKs and runtimes, including clearing dotnet references out of system environment vars, I was receiving an error on trying to launch a third-party program that also requires the SDK in question.

At that point I repaired the installation of V9 (which I had tried previously, before clearing out the sys enviro vars and reinstalling VS), and then everything came good.