You didn't say if you had your passengers in the truck while being weighed. You have 560 lbs. left for passengers.
So it seems your right at the limit when everyone is in the truck. Good job at getting the biggest trailer that's compatible with your truck.
What's your door jam tread act (yellow tire loading sticker) payload? One thing I noticed with the new GMs is that their payload is now very close to my Ford 5.0l trucks 1582 lbs payload (my GVWR is 7350 lbs). Also very similar power output with very similar gearing in the trans and differentials.
Your truck should pull it with ease just add mine pulls my Jayco.
Looked up your floorplan, pretty unique. Nice for just 2 people as the dinette (table and chairs) all folds up out of the way. Maybe when it's just us, we'll consider a similar floorplan.
Enjoy the new rig.
BTW, the 80% rule is right on! When doing the math for payload limitations, it's right there! The 80% is for the capabilities of the truck chassis, not necessarily the drivetrain.