Thanks! That's really interesting feedback and much appreciated. I don't have an Xbox to test on but running it on Edge in Windows seems to work without any crashes, although it's noticeably slower than Chrome and Firefox :(
Perhaps try the following and see if it prevents the crashes on your Xbox. If you're using one of the 3D backgrounds (like chalkboard or collector) try switching to one of the simpler color backgrounds (like classic or dark). Also, maybe try reducing the quality to SD or LD. That should improve performance and hopefully reduce the chance of Edge crashing. These system options apply across all games so set them on a game that works for you (like Donkey Kong mult screen) and then try running one of the problematic ones to test.
As for the controller, I will add native controller support at some point, but you may be able to map your Xbox controller buttons to specific actions. Open the game settings (F3) and then select the specific action you want to map under "Keyboard Controls". It should start flashing. Then press the controller button and it *might* assign that button to the action. I would be interested to know if it does!
Thanks again for the feedback and let me know if these suggestions help.