Got it. Well, sort of. If I (theoretically) disable all display plugins by manually editing the registry, my screen savers come on automatically while Media Center is running. Halleleujah!
Now I guess I'll re-enable each display plugin and see if a particular one is the culprit. Nope, scratch that. Someone else will have to carry out that experiment. Sorry, no time.
Here's how I disabled the display plugins:
In HKLM\Software\J River\Media Jukebox\Plugins I renamed the key "Display" to "Display2." Then I created a new empty key (just in case) called "Display."
Then I went to HKCU\J River\ Media Jukebox\Plugins and did the same thing.
Haven't experimented beyond that.
A couple of extra notes: When MC is running, the screen savers take longer to start. I set them to a minute and they take about 5 or 6 minutes to come on. Also, so far I've only been able to get this to work in restored standard view. That is, if you minimize standard view, it doesn't work. Also, some screen savers still don't work. I got Marine Aquarium 2 to work, and a couple of built-in Microsoft ones (the ones I tried).
Good luck.