Yep - payload is the issue. By your numbers, you have 750 left for your trailer - and some 75 of that is going to be used by the WD hitch. So, your tongue weight needs to be at 675 or less. At 13% tw, that allows for a trailer that's 5,200 pounds loaded. Even if you count on some weight being transferred back to the trailer by the WD hitch, you would still be maxed out in the 6k range (loaded).
Is there any way to move sme weight out of the truck and onto/into the trailer? That could make a big difference (ie - if you can move 200 pounds of that gear from the truck to the trailer, you could up your trailer weight by as much as 1,600 to 1,800 pounds.