Just some thoughts on this. Do you have a catalog system that can show you item locations? At a few warehouses I’ve worked with (and at our own) you are able to store a location ID with the inventory listing. Then you use a pick list system to keep track of what you need to prepare for outgoing. The pick list system will print you out a summary of items to be pull from the warehouse, group items by location and quantity.
Have you looked into a pick packing or pick list system?