As I understand it, private aircraft types were essentially bought…no doubt aided by the seller knowing he wouldn’t be flying for the duration. And not all were impressed, a friend had prewar Staggerwing (as opposed to one built to a military order) that had no military history.

As far as being paid by the hour, that might have happened with commercial aircraft.
However, in the very limited amount I’ve been able to read on this subject, well known historian and author Peter M. Bowers wrote that at the end of the war, an airline with right-side boarding procedures (sounds like a DC-3) received left side door aircraft. He also reported that airlines might have given-up P&W powered a.c. (again, it sounds like a DC-3) only to get Wright-powered a.c. back.