Settling of springs is not unheard of, I just havent heard of it on F150s much. A gas charged shock could raise the rear a bit, so that is also a possible scenario, but I dont think there is a shock you could buy to guarantee you get some lift in the rear.
Cheapest/easiest way to raise the rear will be with a taller block. There are some 3" blocks out there that come with the new ubolts that will be needed, probably ~$150 for that kit. Should net you the 3/4" you are looking for. Next option would be air bags, which could net you a bit of lift if you run them a bit over 5psi, but that could make the ride a bit stiffer, and those kits are $400-$500. However, you get the added benefit of the bags when you need for towing/hauling.