And that would work. He can't stop MPs voting for Badenoch. But if he had enough spare votes he was confident of, he could have "lent" some votes to Truss and Mordaunt, so making more sure that Badenoch came last. All he needed to do to make sure he went through to the next round himself was keep at least 1/4 of the votes for himself - in fact he had pretty much spot on 1/3.
If he has been lending out votes, then he has more support than we can see. In this final MP vote, provided he is sure of at least 1/3 of the votes for himself, then he can "lend" surplus votes to his preferred opponent in the run-off. And so if he was lending out votes, he'll probably want to bring a few back to himself to get comfortably past that 1/3. But if there are any spares after that, he can "lend" them to his preferred opponent in the run-off. Though in this final round, it might be more important to demonstrate to the membership the depth of his support in the parliamentary party, than to choose his opponent.
Tory leadership contests have sometimes swayed in a different direction from how they seemed to be going, as deals are made and compromises entered into. Like when IDS emerged from below, as it were, apparently agreed as the more acceptable anyone-but-Kenneth-Clarke candidate than Michael Portillo.