"The specific details about difficulties with the door seem plausible."
Both aft doors were still attached to th remains of the tail.
Leaking door seals are not unknown. If pressure leaks are severe, it limits the altitude the aircraft can maintain set cabin pressure altitude.
Don't forget, cabin altitude is controlled by the outflow valve, essentially a big, adjustable hole in the skin.
Side Note: pressure leaks were easier to troubleshoot back when smoking was still allowed on aircraft.