I keep picturing Shuten trying to go home while he has the shakujo, and I'm not even sure where home is

Oh I could look that up for you. Some of those old villages might be paved over or starved for cash, though.

So totally. It will be cute, though, because it is Athrun. ^^

He needs someone to kiss it and make it better.
Here is where Kagalli/Athrun fails, as she would just beat him up.