I actually don't think the exchanged guys are legal targets, due to this REG quote:
Played Outside Battle
A set-aside enhancement may be played on a character in your territory, provided the enhancement is played on your turn and it is not played during the Battle Phase, and targets your own character (i.e, it sets your own character aside).
Since you don't own the exchanged-for guys, I don't think you can set them aside outside of battle.
However, if on your block you set them aside with TPBD (since they are legal targets for it when played in battle) I would assume they would stay set aside until SoG is played. If it's played within the next two turns, you keep them for the remaining time. If it's played after two turns, your opponent gets them back (and after two turns, I think they would technically be transferred to your opponent's set-aside area). Regardless of ow long they are set-aside, you get your heroes back after two turns.
I am obviously not official, but this way makes the most sense to me.