An honest explanation of a watch with a missing display due to faulty hardware (after purchasing AC+) = Denial of service, you’re missing necessary hardware, you’re S.O.L.
Or-
Willing to be dishonest/unethical and/or commit possible fraud, purchase a broken watch display from a third party = All necessary parts, Apple may issue a replacement at no cost (but bad karma for sure).
Again, to be clear, I am NOT advocating anyone commit fraud or be unethical when dealing with Apple products requiring service or replacement. Anyone who wants to read my post history will see that I always advise everyone to be polite and honest, even when there is damage due to neglect.
I dropped my iPhone 4 and shattered the back glass three weeks after I purchased it, and I was fully willing to pay the $200 to replace it. I didn’t make up a story or any fairy tale to the Apple employee about how it broke; I was honest in saying I simply dropped it and the back glass shattered. Apple replaced it for free and 15 minutes later I was out the store with a new iPhone.
If the OP’s story is true, then I have to disagree with Apple not willing to make an exception in this rare case, especially since the OP purchased AppleCare+ to accompany the watch. I have always been appreciative of Apple’s stellar customer service, but this one stinks to high hell.