Something to think about: When Enterprise-C came through a rift into the future, thus creating the universe where the Klingons and Federation were at war, the Tasha Yar from that universe went back in time with the Enterprise-C and lived out her life in the main universe, even though she was dead in the main universe and the universe she came from ceased to exist (or was no longer the main universe, or whatever).

Going by that, the crew from First Contact no longer exist (or only exist in the main universe, or whatever) except for that time period where they travel to Earth, meet Zefram Cochrane, etc., because their timeline has been trimmed from existence except for that past loop.

It's a big bowl of timey-wimey stuff. A plate of four-dimensional spaghetti thrown at the wall.