In my mind, the Enterprise is 300m long. The new ship is no bigger than the Excelsior. That is all.
You have to ignore an awful lot for that to work...
Add to that the branching corridors around and behind the bridge.
A nice easy explanation for the ship sizes being so different is that there's a different guy running Starfleet in the alternate reality. Prime Trek had Admiral Nogura, NuTrek has Admiral Marcus. Nogura, for whatever reason, wanted frontline ships compacted from the huge Enterprise-D-scaled vessels of the Kelvin era to Voyager-like sizes (hence the 300m 1701-prime), wheras Marcus kept with the enourmous Enterprise-D-ish (and now bigger) scaled ships.