Didn't an Xbox game actually set it up so the entire processor would reboot and just appear to be loading a level?
You could set an image to display while the console rebooted, so they put up a loading screen and rebooted the console. When the console rebooted, the game knew it was in a "loading" screen, and picked up from there.
Modern problems require modern solutions, indeed.
The real snazzy way would have been to use an older chip in the HDMI processing pipeline somewhere, and let you play an older game on that chip. I believe Nintendo has used older generation chips as sub-chips now and then.
The original xbox didn't even have an HDMI port.
Plus, I believe at that time Namco owned the patent on "games during loading screens".