We are doing truckloads and the reality of Inbound Fees in the USA marketplace is over $2,000 per shipment.
We considered AWD or splitting shipments. However, note that AWD by AMZ doesn’t support food, and split shipments may have similar rates when paying carriers.
I think it would be a better idea if you could ship the items using FBM instead. You can open a business account with usps. Usps agents can iffer you a much better deal at shipping, they would ask for your monthly units shipping out value, if you are doing great then they can offer you a good price. A warehouse would be one time investment or you can do a yearly contract. Hire a warehouse manager to take care of the stuff. It sounds expensive but it is better than FBA. Amazon is just adding cost after cost.
Is everything in the boxes the same? If so, sending them case packed (instead of individual) and selecting Amazon optimized shipping should make it cheaper.