The video export didn't work, until...
Tl;dr ffmpeg was broken, and how I fixed it.
Musescore wouldn't export video scores, and it didn't matter how much I pointed it to the ffmpeg directory, it couldn't find it. (c:/ffmpeg/bin). As I have it, it's looking for a DLL that just doesn't exist anywhere in that folder. I tried editing the Window Environment variables, and nothing. Why didn't I just install it the way the handbook says? Windows wouldn't launch the msi file, it doesn't even open. I Googled, and found how to do it with a command line:
msiexec /i FFmpeg_8.1_for_MuseScore_Studio.msi /l*v output.txt /quiet
This copies the files to the right directory. When I opened Musescore Studio again, ffmpeg showed up and the video export worked. Sigh. Couldn't it just be included as a dependency in the 4.7 update?
Anyway, I found a video tutorial on how to make your videos even better with Davinci Resolve: