Forgetting what could have been, a third party does not need to win the president's office or even have a presidential candidate. A handful of senate seats and a dozen or so house seats are enough to make a huge difference. It will essentially be the tie-breaker or "dampner" party that prevents extremists from wrecking havoc like they are now. Think of it as having a party of Joe Manchin's without the selling out to big coal part.

Not having a presidential candidate at all prevents voters from voting on party lines. They should also prevent the option where you check one box and that means you vote for only one party for all candidates. If you want to do that, do it one by one.

Also, I have a solution for gerrymandering: split a state into a square grid where the dimnensions are set based on a false assumption of equal population distribution. Then adjust the size of squares with less population than the presumed popularion under equal distribution by merging them with a similarly apportioned square segments of a neighboring square with the least population. The result would be a somewhat fairly divided grid where divisions are made by the algorithm and nothing else. Census adjusted of course every few years. What is wrong with this idea? Squares will have less people than others but the difference between them is minimized. The number of house seats depends on the number of squares(or rather square derived parcels).