You’d need to have the business be the arbitar in shipping so if one ships and the other doesn’t ship in a given time the more functional one gets their stuff back and a refund. The nonshipper pays a fee to the business equivalent to the cost of if they had shipped their item.

I bet you could have the business collect the shipping in advance actually, split evenly between parties, and then email expiring labels that would get the packages to the business site and await the partner package. Once both packages are confirmed, they get new labels pushing them to their new homes.