So I spent a day or two trying to find the adhesive, as well as doing a lot of searching on how to reattach the watch face. I found some on Amazon but it was rated fairly low. I then considered going to the Apple Store, but since it was no longer covered, there was a $250 fee. Given that, I considered getting a new Apple Watch, but was also tour as it was going to be $500+.
All of that seems pretty high, especially given the watch itself is still completely fine.
I then realized I had a much simpler, much cheaper option: a watch case.
I got a case online that cost about $10. It didn't really "solve" the problem in that the screen is still detached, but it solved to the extent it made the watch usable again. :)