I'm also getting that same problem with the Exit Doors 1 & 2........let's wait & see what Umberto says/does.
It's more than likely that PMDG (same as with the 747 and the 737 NG) used custom XML variables to represent the door's status so, GSX can't check them using the default FSX variables normally linked to Exit1, Exit2, etc.
This means, to get GSX working correctly, you have the following options:
1) Configure GSX to ignore the doors status, by setting the affected door as not having any checks. This is by far the easiest option, and will result in GSX operating correctly, but without checking if the doors *are* open or not, which means if you forget to open them, the service will start anyway, and you'll see baggage and crew passing through the bulkheads.
2) Figure out the names of the custom XML variables PMDG used, and configure the affected doors to use a custom XML expression with a custom name too. This is explained at Page 28 in the GSX manual. Figuring out XML variable names us usually done by peeking inside the .MDL of airplane with an hex editor. You don't have to change/edit anything, just searching for the name (usually contains "door" string) it's enough, the XML expression is usually very straightforward to write, such as:
(L:MyCustomDoorVar, bool)
Then, assign the custom variable a name same as the one PMDG use to name that door, which will help identifying it.
This option, if done correctly, will result having the behaviour of a natively-supported airplane.
3) Wait for us to add a 777 configuration. I'll try to do this as soon as possible, if only to have a look at possible more advanced interactions between the 777 and GSX beyond just doors, for example with wheelchocks, GPUs, etc.