The payload on my 2012 XL Denali is 1342 lbs, yet we are safely within all limits pulling a 32' 7000 lb camper behind us. A trip to a cat scale at a nearby truck stop will show you where you're at, and will also show how your weight distributing hitch is working. The right ticket below shows our Yukon and camper fully loaded for camping with 2 adults, 2 kids and a dog on board. (The left ticket shows the truck without the kids and dog on board or the camper). We run with a Recurve R3 WDH with 1000 lb bars, and she rides level with the factory rear air suspension. GVWR on the Yukon is 7400. GAWR front is 3600, and GAWR rear is 4200. Even though we only have 140 lbs of payload left, we still have another 220 lbs of margin on the rear axle and 320 lbs on the front axle. This is because some of the tongue weight gets shifted back to the trailer axles by the WDH. In my case, about 220 lbs worth of it.
I concur with the others here that the longer wheelbase of the XL would be beneficial to stability and handling, yet I've seen plenty of people towing long campers with shorties and they report good experiences overall. Gotta remember that the newest 2022 Tahoe has another 4" of wheelbase over the GMT900 generation as well. To the OP, I think you'll be just fine with that setup.