Thank you everyone.
APT is correct, the 1050lbs is the lowest maximum payload for the fully loaded Summit model.
So the consensus for the maximum payload, seems to be to use the GVWR rating and actual loaded curb weight and not the number from the tire and loading sticker.
Since I have neither the TT or TV, I needed to start somewhere, so that is why I am using the published numbers. If there was a scale nearby the Jeep dealer I would definitely go weigh it. I am trying to make sure that I will have some safety margin before buying the Jeep or trailer.
The model of Grand Cherokee we are looking at is the 4WD diesel Limited without any options but tow package, it has a GVWR of 6800lbs. There will just be two of us and a dog and minimal cargo.