How about I make a proposal to start the conversation:
Procedure to move shops:
1) Person buys 2nd shop.
2) Person then immediately puts a sign in the entrance of their previous shop that they are moving, with a date and time not more than 3 days in the future and before their present rent has expired, which will be the time limit to clear the shop. (Time should correspond to the rent sign from their new shop to avoid confusion about time zones.)
3) Immediately after posting the moving sign, all shop signs in the former shop must be broken. (Immediately can be a problem for non premium members if something happens to their connection to the server. The enforced rule should be the 3 day time limit and that only 1 shop may sell items at a time.)
4) Everything must be moved before the end of the day on the sign, at which time a mod could reclaim the former shop, if requested. This date can not be more than 3 days after the purchase of the new shop, which can be checked by the rent sign of the new shop.
5) Person turns off auto renew until after the rent on their previous shop has expired, at which point they could turn it back on. (Need to check that auto renew is by district, so it wouldn't affect their house rent.)
This would require no mod intervention unless someone is abusing the system or if someone wants to purchase the abandoned shop before its previous rent has expired. I invite comments, questions and clarifications, in the hope that this conversation will lead the mods to adopt an official policy on moving shops.