Totally understandable, DnD, and we definitely don't want to make any unreasonable requests.
I understand the list and the swap are separate. Perhaps adding a "next step" page after we finish editing that offers the green buttons and asks if we want to add it to swaps we're part of before returning to the list? Any simpler suggestions?
Your batch suggestion is great. If there's anything else I'd love it would be radio buttons to select for deleting more than one item at once.