They've got the same problem as when changing leaders during the last Parliament.
MPs get to reduce it to 2, but the members didn't choose a leader based on winning an election.
If they can't match those two aspects, it doesn't matter much. They'd be better off making sure that there is only 1 candidate, with the others withdrawing, and taking it out of the hands of the membership.
121 MPs, 26 brand new and therefore unknown, but 41 is enough to be one of the last two.
I'd heard IDS as a potential stand-in (Sunak does the PMQs before the recess, and an interim leader takes over - Hunt seems a good bet for that, but IDS probably could corral them.