I've got a 2015 GMC Sierra with the Max Trailering, 5.3L 6 speed 3.73 axle.
Tow rating is 10,900. Payload (yellow sticker) is 2015.
I pull a Cougar 30RKS. 34'4" from hitch to bumper. Max weight 8,200 lbs. Tongue weight around 1,000 (per a scale). I use a 10K Equal-i-zer 4 point hitch. I'm within all my limits by a decent margin and it tows just fine. I would not go much heavier though.
I do plan to add air-bags more to help with the bounce but it's not necessary.
Last truck was an 01 GMC 2500hd Diesel. It bounced as well and I was thinking of adding air bags to it. just a long trailer for the wheelbase of the truck. I know the two won't tow the same, and that I will have to get used to the motor revving a lot more than the diesel did, but the diesel didn't suit my non-towing life (short commute, never warmed up) so it was time to get new.