FileBot

For example, I currently have my Muppets Show in airdate order. I'm looking to reorder it into production order. When I go to rename and choose production order, it just wants to rename the episodes without actually changing the order.

Yes, you can (1) match by Airdate Order and then (2) rename by Production Order. You could start with the Convert DVD to Airdate Order example preset and then modify that to your needs.