Might be the standard Crossfield, with Discovery and Glenn being modified variants to support the spore drive.

My gut feeling is that with a couple changes this episode would have hung together better-

1. Have them take a shuttle instead of the Enterprise. This lowers the stakes for our command crew and simply makes more sense than half the crew (that wasn't on leave) agreeing to steal a ship. It also means they need to figure out a different way to deal with the fake Federation ship at the end of the episode is some way other than 'shoot it with bigger guns'
2. Have Chapel and M'Benga do something within their character strengths to escape instead of magic drug that lets them hand-to-hand fight their way through a dozen or more Klingons.

That said, there were a lot of things I DID like about the episode, including the Klingon Captain at the end and the new Chief Engineer.

It's entirely possible that there was also a technological leap made not long after the Ambassador was in service, much like what apparently happened with the Galaxy class. It might not have been that the Excelsior production continued at the expense of the Ambassador, but that there is a gap in ships where Starfleet didn't want to build entire new spaceframes that would be unable to take full advantage of new developments. Refitting the massive number of Excelsiors and Mirandas that already existed might have been the stopgap solution until the next generation of ships (Galaxy, Nebula, Akira, etc) was available.