On that note - because the judgment is stayed until Jan 4, and the primary ballot deadline is Jan 5, all Trump has to do is file the appeal on Jan 4. SCOTUS will not respond in ~24 hours, and Trump goes on the primary ballot.
SCOTUS shouldn't then call it moot, because the same judgment will apply to the general election, but they're going to be really behind the eight-ball on this. If they take up the appeal, there is no ruling they can make which will not end in at least vast public uproar. I'm still of the opinion that they will decline to hear the appeal, on the basis of states being the sole authority for operating elections.