So, in a period of a few days (literally), they dragged the Yorktown back, rebuilt all of her internal assemblies, put in a new engine (explicit), decommissioned or reassigned the entire crew (or cleaned up the bodies), re-allocated the ship as the Enterprise, AND were able to get Kirk on it despite not knowing if he would be exonerated at trial?
We really have no idea how much time passed between crashing the Bounty/release of George & Gracie and the trial... or how much time passed between the end of the trial and the crew being reassigned to the new Enterprise. I've always assumed it took weeks if not months to clean up enough to get around to court-martialing Kirk & his crew, and it could've been another span of days to weeks before they were taken to their new ship.
There's any number of reasons why the idea that the Enterprise-A is a rechristened Yorktown is a bad one. But time isn't one of them.