(If there are are two pilots on board both current and qualified on type and can safely reach all controls, they CAN decide who is P1 at ANY time they choose. And must log each portion of the flight they did.
Don't make it complicated.)
They could equally well decide to share the flying in which case they'd be joint P1s. They can't be P1 or P2 on such an aircraft. Why not just log the the total time each with a suitable encoded comment in the remarks column and take it from there. The object is hours I presume and what's the worst that could happen? A division of the total time spent flying together into two parts, based on the remarks column, if anyone ever bothered to pick upon it.
I know that flight schools often work time on the Hobbs but isn't flight time actually taken on the first movement of the aircraft until the final application of brakes? Take off and landing times are for flight logs not log book logging?