if each box has to move separately then I don't think you can do much here.
Before I go much in detail could you please let us know
1) How the physical movement takes place (is he picking all the 30 box at one time from Goods receipt area and then going and dropping all the 30 box to Bin or he travel 30 times from goods receipt area to physical storage bin )
2) Scenario mentioned by you demand pallet to optimize the putaway process however you mentioned that you are not using Pallet, is there any valid business reason not to use pallet ?