It seems the four doors would be placed between the four arms of the center X-shaped pier. Jamming the E-D between two of the X arms shouldn't inconvenience the rest of the dock much, and the necessary maneuvering would be limited to flying straight in nose first and backing straight out stern first. Which is pretty much what we do see.
It's difficult to understand why Starfleet insists on enclosed docks in the first place. But one where they can fit four E-D -sized ships at a time would appear only slightly less useful than one where they can pack four Galaxies
and sixteen smaller ships.