In addition, when I single-click the LSK to close the front left door, FSX does not register that the main entry is closing. It's as though it believes that the 737's main cabin door was never open to begin with, that the aircraft spawned with the door closed, even though the exterior model suggests otherwise.
This clearly indicates the problem is not GSX.
The 737NGX uses the standard main door variable for the main door (while all the other doors use custom variables instead), which means whenever you operates it, you are supposed to see the default green message bar from FSX about the main door opening/closing.
If, as you are reporting here, FSX itself doesn't register it, GSX can't obviously do it too, because they are both relying on the same variable.
So, it really seems the problem is what you already suspected it is: the external model is somehow out of sync with the actual FSX variable that controls the main door, and both FSX and GSX are being fooled by it. When you double-click on the FMC, the variable will go in sync again.
This MIGHT be related to hydraulic/electric issues ( I'm not sure if the 737 uses electricals or hydraulics to operate doors ), so the door's status might have been confused.
