I thought non-prefect players could escort Discards too? (At least, that's what the rules page -says-. `.` )

By a particular interpretation of those rules (and sequence of actions), I'm thinking it would actually be possible for one escort to get both of them... But I can't think of any way to coordinate it without having a person in the other school to pass messages.

And the more I think about it, the more I feel like Yuka would think this is a great idea and try to convince Suzaku to do it. It's a pretty straight connection between her overall worldview and stuff she's already trying to figure out.