I recently purchased GSX Ground Services and had the opportunity to use it twice with Quality Wings 757.
So GSX worked with this one.
But when I tried to use PDGM 747 and Level D 767, I would get "Fatal Errors" and the system would reboot.
This seems to answer your question: the crash doesn't have anything to do with GSX.
This appears to have started after I installed GSX Ground Services. The fatal error seems to start when I request ground servicing. Is there any way to trouble shoot this problem? Attached is one of the Fatal Errors I obtained from Windows Event Viewer (Which I just learned about). I cannot make heads or tails of the problem.
Your log shows that FSX.EXE is crashing in the API.DLL file.
It's not possible this could be caused by GSX, since GSX runs entirely external from FSX under the Couatl.exe program and, by definition, an external .exe can't crash FSX.EXE, that's the main advantage of running as an external .EXE (in addition of not stealing any of the FSX memory).
And, fact you said that GSX worked with the QW757 and the crashes happens only with those two airplanes, further indicates the problem doesn't have anything to do with GSX, fact you noticed it after installing it was purely coincidental.
Also, nobody ever reported a crash of that API.DLL file here. Usually, crashes caused by scenery objects or bug in the video drivers or problems with FSX settings cause crashes with G3D.DLL, which FSUIPC helps to prevent, but API.DLL crash is not very common.
I'd start with resetting your FSX.CFG to all default settings: just remove the %APPDATA%\Microsoft\FSX\FSX.CFG file so FSX will rebuild a new one with default settings from scratch.