I've tried parking my PMDG 777 at several large gates but I always get a message that it's too small for this aircraft, it's the same with the NGX at small or medium gates.
No, you don't "always" get that message. You only get it at parkings which ARE too small for your airplane.
The 777 is very large so you won't find *that* many parkings (but there are some, even without modifications), but with the 737NGX I can count the following:
Terminal 1 - 11 gates in total, 2 too small
Terminal 2 - 23 gates in total, 3 too small
Terminal 3 - 16 gates in total, all usable
Terminal 4 - 34 gates in total, all usable
Terminal 5 - 24 gates in total, all usable
Terminal 7 - 12 gates in total, all usable
Terminal 8 - 40 gates in total, 8 too small
Jetblue Apron - 3 gates, all usable
Deicing Area - 1 gate, usable
Cargo areas - all usable
With the 777, I can see many usable parkings at Terminals 1, 3, 4 and 7 (and some in 2 and 8 too), plus all Cargo areas of course, without doing any changes.
GSX reads the AFCAD and, there are many reasons why AFCADs have a certain size, one of them is that in order to have animated jetways working correctly, parkings radius shouldn't overlap too much, otherwise FSX will consider the jetway to belong to the other parking and will not animate.
I have used the utility to change the gate size to the current aircraft and it then works.
That's why we have that option in GSX. To override the AFCAD radius, which might be too small for many different reasons, jetways, controlling AI assignment or just a bug...
I don't get this at Aerosofts EDDM in the heavy gates. Why is KJFK like this?
Since they don't have animated jetways, it's likely they don't put so much care into setting the parking radius correctly, so they just set them to be fairly large and sidestep the problem.