Yes, the A321 it's ok, and it IS working, no idea why is not working for you, but as you can see, another user fixed it by using a different key and, as I've said, it's nothing related to GSX, which doesn't act on the doors, it only READS their status.
About the difference between the default A321 and the 737/747, is that BEFORE installing GSX, the 737/747 had their aircraft.cgf file wrong, preventing the use of the EMERGENCY doors (but the cargo doors would still work), because they had their number_of_exits wrongly set to 2, GSX installer fix it. The default A321 has always been correct form the start, no need to patch it.