Yeah, that corridor sounds like the main reason for wanting to move Main Engineering...
In theory, we can move the facility aft until the lower end of the core protrudes into the main cargo hold. But we never saw the forward wall of that hold, so we can move rather far back that way.
Also in theory, we might run out of space no matter what; but in practice, both the corridor and the aft end of Main Engineering were created by using forced-perspective mattes. It shouldn't be difficult to decide that some of that forced perspective was "forced for real", and that the corridor and the aft end of ME were indeed shorter than they looked, and possibly only as long as the actual physical sets.