Reinstalling all of your products is not an option I would eagerly look forward to. Especially since they have been working fine for years, as evidenced by the fact that this is the first time I have felt compelled to contact you for assistance that I can recall. I believe the issue lies with the "disappearing" Couatl entry. Not sure what to think of that. Any assistance would be appreciated.
Then you should create a DIFFERENT post, because as you can see, this one doesn't have anything to do with your issue. This post is about the Addon Manager NOT loaded in FSX, yours is (according to your report) that Couatl crashes only when you go to an FSDT airport.
They don't have anything in common, so you should open a separate post about it. In fact, I did it for you, and created a separate post about it.
Since you say you HAVE both menus at start, and it's just Couatl quitting when you go to an FSDT airport, the first thing to do is to enable Logging in the Troubleshooting section of the GSX Settings menu and restart FSX. Then (after Couatl crashes), exit from FSX and check your %APPDATA%\Virtuali folder for a Couatl.LOG and a Couatl.ERR files. Post them both.