How do I set the cover photo of a "shared" Photos album? I understand how to set the cover ("key") photo of an Apple Photos album, but I can't see how to change the cover photo of a "shared" (copied) album.

How do I set the cover photo of a "shared" Photos album?
You can't.

With shared iCloud photo albums the key photo will always be the photo that was uploaded last.

Update: This is still valid for iOS 12.1.2.