TMs woudn't sort it, they would have to change how they pick it. Pick everything for a custom block, dept number, item type all at once, and then instead of loading the merchandise directly onto a trailer, they would shorten the conveyor belt, have an empty pallet at the edge of the trailer, and somebody would build pallets, and load them pallet by pallet.
I think the most efficient way of doing this would be to split up grocery from everything else - and have trailers make stops at multiple stores. For example, have a trailer loaded with food, hba, chem, paper, pets, baby hardlines, have pallets for two stores on them, and stop by one store to unload and then its other store. Then the following day, it could drop off everything for general merchandise, softlines, electronics, domestics, housewares, toys, sporting good, seasonal, on the other days. It would especially take the strain off 6am stores - if the merchandise was unloaded the day before, and you only took half a trailer's worth of merchandise every day, you could run the flow team with fewer people, you could work those people more days of the week, and you could give key performers on flow more hours on flow itself.