The PMDG 777 is internally supported and doesn't need any further customization so, in order to be sure you haven't made some kind of mistake editing it, use the Reset option in the GSX Aircraft editor, and Restart Couatl, then try again.
Also, we noticed that, after loading a PMDG airplane, the Simconnect menu (which is NOT the "GSX Menu", it's a menu shared by all apps), sometimes gets resized automatically to a small size, so users believes GSX has a problem with the menu, when in fact it has only been resized by having loaded the PMDG for some reason why don't understand, but it doesn't have anything to do with GSX, since the size of that menu is not under our control.
Of course, it can be resized manually.
Other than that, there are no reason why GSX would work with the 737 and not with the 777, since they are both supported, and are probably the most tested ones, and nobody ever reported a problem with it.