The big problem was killing Kirk. I think had they done a story that brought Kirk into the 24th century, and they had an adventure that required Kirk to do something other than fight Picard's battle and die, which anyone could have done, it would have been much different.
Maybe something that involved a sequel to a TOS episode in the 24th century. There were a bunch of things. Maybe something happens that requires Kirk, but Kirk disappeared in the 23rd century shortly after the events of ST6. Perhaps Kirk's disappearance actually occurs because he was needed in the 24th century.
Or expand the story that doesn't just have Kirk, but have Kirk with Sulu, Uhura and Chekov at the time. Perhaps they were searching for Scotty, and we meet up with Scotty, Spock and McCoy in the 24th century, where whatever the plot device is, has both ships uniting. In fact, they could have done a story that combines a TNG episode with a TOS episode so each crew helps the other solve the problem.