Alas, it seems to preclude Excelsiors much greater than 500 m in length, mainly due to height issues. Unless we assume the great ship tilted her bow up and stern down when emerging... And even that gives rather little margin.
She may have simply turned diagonally to fit through the doors. It's a space ship, no reason it has to be oriented the same way all the time.
OTOH, we did see the Enterprise-D go through a set of doors on an identical starbase with similar clearance. We should consider the possibility that the doors on one side of the shroomdock might simply be larger as a matter of course than the doors on the other side and Excelsior caught up with Enterprise after quickly slipping out through the "big door" 90 degrees farther around.