That’s how it was presented to me, that Joe acts until it is determined who is qualified. If it follows history, it will be a vote in the House of Representatives that will decide the issue.
The question is who’s names will be on that ballot?
From my memory--only--and this is not what I do every day--
The names of the top two (or maybe the other vote getting candidates and then after a ballot state by state, it gets to the top two) vote getting candidates. That may have been modified by amendment. If not, the argument about McCain's eligibility becomes relevant--I think it is equally clear that McCain is not eligible although I know that is not a popular position here.
And as I recall, contrary to your statement, I think it is a state by state vote--with the state's ballot determined by majority vote of the state delegation in Congress including the Senators but that may also be wrong.
But if I am correct, and further correct and McCain is ineligible, you get down to Bob Barr and others.