Yeah a few things need to be clarified. Either something is wrong with your truck and the shocks have failed, or you are just using an elaborate excuse coming from a four corner coil suspension truck to buy a new leveling suspension (that is what you listed, not a factory replacement that is catered to a good ride). The Ram uses coils, it will ride nicer period. But you say the Silverado rear is super soft, it will sag less with weight on the hitch than that Ram. The Ram suspension is catered to the suburban crowd who never haul/tow much, the Silverado is the other way and it geared towards hauling and towing, similar to the F150. Now yes the shocks aren't the best but to say it is the worst means you have never driven or ridden in an actual truck from just a decade or two ago, as those rode even worse (some weird combination of rough and floaty). Trucks these days ride so much better and are better controlled than back then, with the newer steering systems, coil over struts and new computer aided design simulations means things are much better. Not sure how people can say anything from today is worst than decades past, this also applies to headlights. People complain the halogens are crap, well they much have never been in an sealed beam vehicle before as I promise those are much worse.
Either way, take it to the dealer and have them check it out and make sure nothing is wrong. If it is ok and you just don't like how it rides then replace the shocks if you see fit. How a truck ride isn't for everyone and each person has their own flavor. Some like it rougher, others want it smoother. Air suspensions are being added because people are buying these things less for truck duties and more for image contests and they want them to ride like a luxury car since they don't do any real work.
A piece of advice, some of the best riding suspensions are the higher end off road shocks and springs from King, Dirt Logic or Fox. The truck will roll more but will soak up bumps like no other, that is why Raptors are so popular in the suburbs. They don't need the carrying capacity which is why towing and payloads are down but the ride is very nice.
Tyler