The area in question was between watertight bulkheads K and L. On the starboard side were cabins E-69 through E-75; the engineer's mess was on the port side. Both areas had the same issue. There was a way out, though, even if the manually-operated watertight doors were closed. The doors near the aft bulkhead (WTB L) led into the reciprocating engine casing, which contained catwalks and ladders that aren't shown on the Beveridge plans found on this site. I can't find a drawing that shows the catwalks in the engine room space, but there's one for Boiler Rooms 1 and 2 here, showing the ladders that led up to A Deck.