I think I can give some perspective here.
Our previous tow vehicle was an Expy. A bit older than yours, but similar specs. Now my daughter's commuter. It is set to tow: LT tires, front / rear larger swaybars, and factory tow package. About as good as that rig gets.
Our trailer had a dry claimed weight of 4800lbs. My experience is that I didn't want to go any bigger with that vehicle. Now this includes four people in the truck and two dogs and gear. But not any unusual loadout. We were also at about the payload limit. Yellow sticker 1450lbs.
New tow vehicle is Suburban 2500. And it tows that stupid trailer like it's not even there. Must be time to go bigger.... :-)