> OTOH he could run for VP.
No, he can't. The elected VP also has to be eligible to be elected as president.
The 12th Amendment says:
> But no person constitutionally ineligible to the office of President shall be eligible to that of Vice-President of the United States.
Paired with the 22nd which restricts Presidential eligibility, Trump cannot be elected as VP. He could potentially (this would go through the courts, it is a gray area) be nominated to VP, but he cannot be elected as President or VP again.