I don't carry boxes, but I do carry a couple of half height jerry cans up on my Yakima LoadWarrior.
I use rachet straps. I always keep 10 or so in my rig stored in a Harbor Freight zip bag. Most of my straps have been cut down and the end bummed to stop fraying.. around 6' I think. Gas cans, the blue Coleman water jug, firewood, trash, traction plates .. all secure with ratchet straps.
A little off topic.. I carry firewood in black canvas bags I got in Amazon. Then, the next morning I put my trash (and sometimes other people's trash) into the bag and it goes up on the rack. No mess in the truck. I have 3. You can put 1.5 of the grocery store firewood bundles into one bag.
This:
Firewood Log Carrier, Gonex Durable and Waterproof Nylon Log Tote Bag for Fireplaces & Wood Stoves, Extra Large(25.6x11.8x10.6inch) Black ...