No, I think the hanger in JJ's movie is more of a private hanger for the students to get to their ships, this is more of a public train station kind of thing. Besides, most of JJ's "behind the ship" scenes are a bit too industrial to match the rest of the movies/series. JJ liked the real world locations for those kind of things.

We can't really use anything from JJ's movie, as he changed so much for this alternate timeline (look at where the Golden Gate Bridge is in location to his Academy!). It's a shame really, but it is its own self-contained universe with its own continuity. We need to make good with what we have from the rest of the movies/series.

And yes, there are issues with that matte from Star Trek 4. Never noticed that the building was floating, thanks for that. It needs work, as you can see. It's all up to FF really, if he just wants that matte fixed, or if we can make a whole new one using elements from the later versions of Headquarters.