Sounds like you got a similar setup as I do with the 48"x60" basket and a Jet box.
Here is my setup.
I drove to Alaska two times like this. I had around 650-800lbs of junk on the roof. But I spread the load out between 4 low profile Yakima cross bars. When I drove to Alaska this was on the roof basket: 1 full size spare tire for truck, 2 spare tires for trailer, 3 fuel cans totaling 30 gallons of gas, most of the time I only drove around with 12 gallons on the roof. Couple camping chairs. In the box: clothes, some tools. In the trailer: sleeping bags, pots, pans. Inside of the truck had a fridge behind the drivers seat and a cooler of food right behind the front center console. I have captains chairs second row. Inside of the truck was virtually empty.
With 6 people you have enough space to stuff everything you will need to a month behind the 3rd seat. You just have to have tetris precision when packing and unpacking every day. A dog adds another challenge to the trip. What kind of dog? Is it a big or small dog? If it's a small dog you can get a cage and keep it in the back on top of some bins, which make daily routine of unpacking and packing really quick and easy. If its a larger dog, it will need more space, 100lb lab will need at least 1/2 of rear cargo area.
We traveled several times with 5 of us and a pommeranian and a lab comfortably for a couple weeks.
35" spare donut in the cargo basket. My basket is 36" wide 72" long and Ski box is 18" wide
Box side view
Since you will be traveling in lower 48, I would pack as minimalistic as you can. I would start by figuring out how much space you want to give your dog. Then get plastic bins: 8 of them that will fit in the remaining space behind the 3rd row. One bin for everyone and one for truck tools and one for camping gear/mess kits. Put bulky stuff like sleeping bags in the jet box, camping chairs in the basket. I would stay away from soft sided bags, they don't really last and wind noise is really annoying.
Good luck and we look forward to your trip and pictures.