That scenario is even better. Because the VP would not even have to be likeable enough to fit the VP slot in the general election.
You just have to pick a crowd pleaser as VP, replace the VP, drop the P, and you can put anyone on the throne without a problem.

Congress could throw a spanner in the clockwork, but since roughly half of them belong to either party, you only have to influence (bribe or blackmail) a handful of other congressmen to get a yes vote. And since politicians all have skeletons buried somewhere, that last part shouldn't be a problem.