What happens to songs improperly marked 'Apple Music'?
Figured I'd answer my own question. I made two attempts to contact Apple Support and another attempt to post to Apple Discussions, with no results. 

So I copied my entire iTunes library to a backup disk, and did my best at keeping notes at how many songs I had, which were what status, etc. I knew if things went south, I'd have quite a project in figuring out what songs to restore, but couldn't think of another alternative.

After I finished backing up, I loaded my original desktop iTunes library, and picked "Update iCloud Music Library".

It took about 90 minutes for 6,177 tracks, first analyzing music, and then uploading to iCloud. And the end result is that it looks like it resolved matters perfectly.

I've seen other articles from the past indicating that "Update iCloud Music Library" only led to partial success, and led to people doing long involved processes like opening a new library, deleting all their tracks there, and then going back to their original one to re-analyze and download, but to me that seems more error-prone and unnecessary.

Brief stats: Before I did the update, I had:

Apple Music: 2912
Uploaded: 2486
Matched: 8


After the update, I had:

Apple Music: 43
Uploaded: 3135
Matched: 2228


The rest of my songs stayed consistent in status (Purchased, Ineligible, No Longer Available, Waiting, Error). So far I don't see any songs that are improperly categorized, and all of my personal recordings are properly Uploaded.

I still don't know what would have happened if I had canceled, but matters seem improved now.