Glad that you found the solution.
Since HA uses RocketLauncher in the background, some of those global ingame settings like global exit are there as you have found.
Esc is always bad for RL exit key due to how some emulators use it for other functions like change fullscreen and so on. Then using only a controller inputs combo for RL exit is risky because we noticed with time that xbox 360 inputs work, then xbox one controller and others not. So the safer bet that worked always was using instead a keyboard exit key, paired with a default joytokey profile where pressing back+start with a xinput controller = pressing letter "Q" on keyboard.
We might try to change the keyboard key to a less common one if we reach a conclusion for a good alternative key used on every keyboard.