Not sure about what version you are using, but I just tried the emulator and it has a "Start in Fullscreen" option. With that ticked it worked without issue. I do not use this emulator so not sure if what I have is old or the latest version.
If that does not work for you, try putting the AHK below in the "Running Auto Hot Key" tab in your emulator setup within Launchbox. I believe when you use the controller automation in Launchbox it sends Escape which is why you see it dropping out of fullscreen when you use it. This AHK will make Escape key act as Alt+F4.
ESC::
Send !{f4}