Hmm, the Select and Start buttons must also be generating a keyboard event which is why the keyboard mapping gets overridden :( For now I've uploaded a new build with these mapped by default. So far, it seems that buttons 8 and 9 are generally mapped to Start and Select (although that is only based on three gamepads tested), so hopefully it will work for most controllers. And of course people can still reassign them to the correct buttons if that's not the case.
As for performance of the Edge browser on Xbox , not sure how much more I can optimize the WebGL to improve the performance or prevent crashes. I need to do some more research.
I'd like to create a profile for the button names for your XBox controller on PC, so if you have the time, maybe you can do something similar to this post?