I noticed that the 360 was backwards compatible with Sega GT 2002, and thought that the version with Sega GT and Jet Set Radio Future on it might be too. Seeing as how you boot into a main menu, and then launch a selected game on the disc, I thought maybe after it loads the menu, you could swap a disc with the same structure, but have a replaced GT xbe with some other homebrewed one.
Of course it's late, and this is me talking out of my ass. I have no idea how MS verifies the disc, and thought maybe they would have been dumb enough to only do it at the first boot-up. I doubt that's the case, but I don't have the disc to try it out
Here's to stupidity, and dumb ideas