The shocks will only help if there is adequate load support from the leaf springs. If not there will be too great a range of motion for the shocks to be 100% effective. From the picture posted it looks like the rear of the truck sags down and the bed is not level. If this is the case I would go to a spring shop and have the factory leaf springs replaced or a new one added to support the load. It is not at all unusual for leaf springs to fatigue over a period of years and no longer support the load they could when new.
If your truck does not have an anti-sway bar in the rear then adding one would also be a good investment.
I would also put in as much air in the rear tires as Ford recommends as too little air and there will be more sidewall flexing which hurts both handling and fuel economy.
Although you do not have an extremely heavy trailer load it would still be advisable to have a weight distributing hitch to try to transfer some of the weight to the front of the truck.