I was hoping for some help on determining why GSX will not start in MSFS.
Does this means it doesn't start "automatically", but it does if you start it manually ? Because, if it didn't started at all, you won't even be able to see a log so, fact you have one, seems to indicate at least it does start so, please confirm if this is the case, that it does start, but not automatically.
If that's the case, it's a completely different issue than being "stuck on loading", they are completely unrelated issues.
The log you posted didn't show any errors, it simply show you started the sim with the PMDG 737-800, then switched to a C152, went to KSAN, and exited the sim without doing anything else, it's not even clear if you actually arrived at the airport loading screen, or you quit when you still were on the main menu, after selecting KSAN. That's what I can see from the log, so it might be helpful to know exactly how you made it.