Doesn't the 12th Amendment preclude that end around?

The last sentence of that Amendment states:
But no person constitutionally ineligible to the office of President shall be eligible to that of Vice-President of the United States.

Most would say yes, but it's not as clear as the prohibition against him running directly for the office.

Technically, the 22nd Amendment prohibits someone from being elected twice to the office of President. But it doesn't say that the person is ineligible to hold the office. So one could argue that there's no problem with Trump being elected (or appointed) to the office of Vice President. Once there, he could then take the office of President should a vacancy arise (again, the 22nd Amendment prohibits only election, not holding the office a third time).

The other, more complicated path that avoids this problem is if he had the House appoint him Speaker, ran a pair of compliant puppets as Presidential and Vice-Presidential candidates, and had them both resign simultaneously. Then he would assume the presidency again, bypassing both the 22nd and 12th Amendments.