Free stuff first. Start with the correct tire pressure, if you can get a weight first, great. If not start what the sticker says. Don't exceed the pressure on the sidewall. Then the Cheap Handeling Fix. Simple to do if you can turn a wrench. It may help, if not you have only a hour of time, or less invested.
Hellwig sway bars at
sdtrucksprings.com. Do the rear first. It is a secondary bar to the OEM. You can DIY but it is a job. If you decide to do the front one it still is a job but not near as bad.
Trac bar (panhard bar) ar
ultrarv.com. You can also DIY but can be a job. You sound like it isn't needed.
Safe-T-Plus also at UltraRV. Then again you don't seem like wandering and steering issues isn't a problem.
Has been said alingment. Might help but remember on a solid axel all the can do is the toe-in and camber. Be sure they can check your rear for proper tracking.
Good luck