More useful insight:

I've manually deleted cache files as suggested by @OneEagle above. This did not fix the original Covers problem, but here's something new:

• In Designer > Cache the checkbox for DISABLE PAGES COVER remains checked (unchanged since last night).
• I found that I now have an upload button for the Persons Cover image when looking at /view-persons-profile/[profileName]. I am almost certain this was not present before deleting cache files manually (though, I also did a Dashboard > Clear Cache yesterday - it's possible that the GUI-driven Cache Clear did this last night and I only noticed it this morning after manually deleting cache files. )
• In the Persons Profile, the cover image remained default [blue texture map] while in Persons Home I see my previously uploaded Persons Cover picture.
• Here's the revealing part: I then uploaded a new image from the View Profile page. I intentionally chose an image different from the one that was previously only visible from /persons-home. And now, both views are calling the same (new) image file.

This really did smell like a cache problem, but because I cleared caches manually at the file manager level, I have to conclude that there may be some bug related to file naming in the database table that's serving images to these two pages. But now I'm getting way out of my depth.