A 36 foot camper is going to be a beast to pull with a 1500. I pull a 24 footer with my 2017 Sierra (identical to yours). It weighs out at 5800 pounds loaded with propane, water, beer, gear and food. My total weight on the scales is right at 12k with 2 adults, 2 kids, one real dog, 2k generator and firewood.
I live at 7700 feet and go over 11k feet regularly to go anywhere. This setup pulls well, stops well and parks well.
If I went up in trailer size I would go 3/4 ton or up the specs on my truck. (Max tow and 6.2)
I’ll go out on a limb here and guess that if your wife insists on a 36 foot camper you will also be hauling ALOT of stuff with you. Your situation doesn’t seem like it will be “minimalist.”
Towing at max will be stressful, dangerous and exhausting. I towed my trailer 4 hours home from denver without a weight distribution hitch and it really worked the truck.