Didn't think of making Jack Crusher the captain of the Stargazer because IRL canon, Picard is the captain of the Stargazer. But it is an interesting thought. I don't want to wipe the actual Yesterday's Enterprise from canon because it was so good, so Rachel Garrett remains captain of the Enterprise-C ITTL. I wanted to bring the Stargazer into live pictures ITTL because it's constantly mentioned as a part of TNG canon but we only hear about it through Picard's memories of his service on the ship.I would have used Yesterdays Enterprise as the basis for Generations. Flip Picard/Crusher so that Crusher was the CO of the previous Enterprise, with Picard his XO.
IOTL, Crusher dies, sacrificing himself and the Enterprise to save Picard and his crew, but securing peace with the Ferengi or Cardassians. Unwittingly Picard stops the destruction of the Enterprise, returns to the future and we get something more akin to Yesterdays Enterprise.
The catalyst for the alteration could be something as simple as Picard and an away team on a shuttle being sucked through the Nexus and sending of a distress call, old Enterprise responds and isn't in the place it was originally destroyed at.
Picard, prompted by Guinan, eventually realises this and has to find a way to get back through the Nexus to stop himself sending the distress call to ensure the previous Enterprise is destroyed and Crusher killed.