I checked this at BGTL, and I cannot reproduce it.
I'm using all default scenery with a default airplane so, normally, GSX won't even be able to use this airport, since the default AFCAD has no parkings, so you cannot even call GSX and should see a warning about this.
However, I couldn't see any stuttering, fps was very high ( more than 130-140 fps ) and CPU usage was normal, Prepar3d.exe is about 30% and Couatl.exe was about 7%
couatl was using more CPU (10%) than P3D4.5 (6%)
This is not normal, and unheard of, and regardless of GSX, the simulator should use MORE CPU, 6% is way too low.
In fact, this might very well be the cause of GSX stuttering. The way Simconnect works ( with all add-ons ) is the simulator ITSELF is acting as a master "metronome" for all the add-ons, and it's supposed to send notifications to each ones every frame, or second, or in other kind of events. But since in your case it was taking so few CPU cycles, it's possible it's not sending out all the notifications it's supposed to, and that what's causing stuttering, since GSX is waiting for the simulator clock to update its animations.
Are you running with a custom AffinityMask ? If yes, try to remove it.
If you are using Hyper-threading in the BIOS, turn it off, because it usually improves smoothness in P3D4.