First, My sympathies.
Lots of different approaches could be used, but as one person pointed out-these people may bad mouth you to others, and I'd hate you to get bad word-of-mouth in New Albany. You may not be able to avoid this as some people will be unreasonable regardless, but I think the approach suggested:
I would suggest that you politely take the person who pays the bill to the side and explain that it disrupts your service to accomidate their request. You appreciate their business but during the peak hours you will not be able to accomidate going forward. If they want to come in at a non peak time you can accomidate, business permitting.
Combined with a plating charge for non-peak hours, sounds reasonable if you explain that this takes a huge amount of extra time for your staff to prepare their party's meals.
Deb