I figured out the simplest way to do this and it's working great. Before doing any of this, just make sure you have a backup copy of your iTunes library. It's not as if this is risky, but you should have one anyway.
* Turn off iCloud Music Library on your current and default iTunes library. Then close iTunes.
* Create a new iTunes library by starting iTunes with the Option key held down. Just give it a new name of your choice.
* Go to Preferences, turn on iCloud Music Library, and wait for it to finish loading/syncing.
* Go to My Music, select Song view. Select All, and hit the Delete button, and confirm.
* Now you've got a new iCloud Music Library that's empty. A nice clean slate!
One thing I wasn't sure of is whether my For Your section would change at all, and it hasn't. Apple originally built it's For You section for me based on my iTunes library, and even though I now removed all of it, the recommendations haven't changed or anything. So I guess it retained all that data it already got about my music collection.
The reason I wanted to do this is I hate redundancy. Couple that with Apple Music's tendency to botch song matching and album art, and things become messy really quick. I hate having my library uploaded with botched artwork and mismatched songs (live versions) when there's perfectly intact versions of most of it already on Apple Music that I can add to my Apple Music Library.
Now I can just drag in any particular albums that I own that are NOT on Apple Music in order to fill those gaps. Then if there is any mismatched songs or artwork, I'll know immediately and can fix it easily as I go, instead of scrolling through a huge library of wildly wrong artwork and not really knowing which songs are matched wrong until playing them.