In the Bush v Gore matter, the election had already occurred. In New Jersey, the election had not happened yet (although I can't recall if early voting had already started).
So I don't think is a foregone conclusion that it is a federal matter, and that the SCOTUS will intervene before an election occurs.
Furthermore, Article I Section 4 (Legislature elections) says:
"The Times, Places and Manner of holding Elections for Senators and Representatives, shall be prescribed in each State by the Legislature thereof;"
Article II Section I says (Executive elections):
Each State shall appoint, in such Manner as the Legislature thereof may direct, a Number of Electors...
So, there is plenty of evidence in the Constitution that federal elections were meant to be state-by-state matters. SCOTUS should tread lightly here.
-PJ
I would hope that your scenario is more accurate than mine. But I hold no hope that Alabama is going to keep him off the primary ballot.