I'd add the load to the cab of the truck and if it didn't all fit, add a front receiver hitch and carry basket to carry the rest. Loading the front axle more won't hurt any more than another passenger or two would add. Even though the front receiver hitch and basket have even more weight, shifting off the back axle to the front is the way I would go.
Otherwise, tow a small trailer.
I have a rig similar to yours and flat tow a small car and occasionally up to 2500 pounds of loaded trailer. No problems. In fact, my rig handles better towing.
