I added a Trail Air pin box and my trailer, and didn't really notice any difference in ride quality. If I were doing it again, I would go with an air hitch.
2012 RAM 3500 Laramie Longhorn DRW CC 4x4 Max Tow, Cummins HO, 60 gallon RDS aux fuel tank, Reese 18k Elite hitch 2003 Dodge Ram 3500 QC SB 4x4 Cummins HO NV5600 with Smarty JR, Jacobs EB (sold) 2002 Gulf Stream Sea Hawk 29FRB with Honda EV6010
Once again SHOCKS, SHOCKS, SHOCKS!!! Bounce is a result of lack of dampening, you need a great set of shocks. Bilstein 4600 or 5100 all the way around.
ON EDIT: in addition your pin is a bit light less than 20%, you really need about 22% to 25%. On our 12,360# 5er I run a 2,600# pin.
Russ & Paula the Beagle Belle. 2016 Ram Laramie 3500 Aisin DRW 4X4 Long bed. 2005 Copper Canyon 293 FWSLS, 32' GVWR 12,360#
So scaled your truck weighs 11,756 pounds with fiver hitched? What is the trucks GVWR? My guess your right at max or very slitely over. I would first consider getting a air ride hitch or air pin box or one of the MorRide pin boxes. That made more difference than anything else for our fiver.
"5th wheel bounce"? Are you referring to the back and forth motion like when you go over a dip, or bridge approaches? Or does the 5th wheel not pull well?