Good news! Taking the advice of several on this forum, I covered all the Stainless Steel on the watch, and took a Scotch Brite Heavy Duty pad to the screen. Sure enough, after about 30 minutes of rigorous grinding on the display, I had fully removed the outer AR coating, and the scratches I had are no more!
I think it's UTTERLY stupid that Apple put that coating on. It makes your watch look as if it's easily scratched, and doesn't really gain all that much. I don't really notice fingerprints any more without the coating than I did with it, but I sure do notice the lack of scratches.
At any rate, glad that the sapphire wasn't scratched!