Replenishment Scenario

I am trying to figure out a workaround for a replenishment scenario. We replenish to equipment that uses trays to hold products in a vertical configuration. The process the warehouse uses is to pick the replenishment cases onto a pallet in pick sequence order from the reserve locations. The pallet is placed at the equipment for putaway at a later time, however all the putaway tasks are completed on the RF when the pallet is placed.
Later in the evening the trays in the machine are called down and the product is replenished into the tray.

The challenge is that the cases are on the pallet in the order they are picked from reserve. During the physical putaway process an item with cases at the bottom of the pallet might go to the same tray as a different item on top of the pallet. Therefore, the same tray is called down multiple times. Our warehouse asked if the case picking from reserve could be in the order the items get putaway even if this results in an inefficient travel path for picking reserve cases. I have not found a way to do this in the replenishment