The interesting thing here is that the Excelsior was in production before transwarp had been tested - namely, NX-2000 had been completed. Not just thrown together to perform experiments on transwarp, but completed. As in, she even had all her guns fitted.
What is singularly uninteresting is the fate of the former crew of the Yorktown. It just isn't relevant or realistic to worry about what happens to the "former crew" of a starship; in the real world, no such thing even exists, and personnel are constantly being shuffled between vessels and other assignments. If the skipper of the Yorktown is told to move to another assignment because Kirk needs his or her ship, and he or she complains, that only goes to show that he or she is not fit to serve in Starfleet. Or in any real-world military at least. Or basically any other real-world organization, for that matter.
And really you're not talking swapping out all 400+ crew; just the CO and XO and the Department Heads. Not even a dozen people tops. So even if it is Yorktown, and some of the crew on board might get bitchy that their ship got renamed, it's really not that major of a issue. Plus, maybe not every Captain is as attached to his ship as Kirk. Maybe they are just assigments and nothing more: "Oh I have to transfer out to a new command? When and where...and tell Kirk the deck shimmies when she hits warp 5 and we never did get the damn log-recorder to work right after that last software patch"