Yeah, uh, no. I have a 1997 K2500 gasser which should have the same suspension as your 1996. I added air bags and a rear anti-sway bar, along with the highest weight rating tires I could find. I am right at my weight limit with my Lance 1030. The 'weakest link in the chain' being the carrying capacity of the tires.
I looked up a Lance LC980 - that is no small camper. I suspect you will be at or over the weight limit of the tires with just the camper, much less with the trailer tongue weight. You really need a dually haul that combined load safely.
That said.... "Could" you do it? Sure. I see overloaded SRW's with campers & trailers all the time. I cringe a bit and give them some extra space - not something other drivers realize they should do. Just because the diesel under the hood can move the weight doesn't magically increase the carrying capacity of the tires.
Am I here to be the "Weight Police"? Nope, but you did come here for advice. You do what you want. Good luck!
-Eric
