So lemme get this straight, you bought the most heavy duty truck available, generally speaking, a truck designed to haul and tow heavy loads and you don't like the stiff suspension? Really? What were you thinking?
Just messin' with ya! I feel your pain, everyday!
Look, there are no simple, cheap solutions. Once you go down this road, there is no stopping or turning back. You will have to spend hard earned cash. You might piece meal your truck and find that your original plan has changed over time and experience. What you are not looking for is a lift kit, but a suspension modification. First you change the shocks and then realize you want more. Next you will want to add larger tires or want to level the truck, which may make the ride stiffer yet. Unfortunately, to do what you want will cost you, probably more than you want to spend but there it is. Having said that, I am modifying my suspension for similar reasons but perhaps different purposes in mind. I went with a Carli Suspension mod. Yes they are pricey and may not be what you want to do but you do not need to spend the big money on their most radical suspension. Have a look at the Performance or Backcountry kits or even the starter kit. In the end, saving for a few more months might not only encourage you to upgrade but help you appreciate it all the more.