I don't know why people spread mis information like this. The gen2 Raptor does not weigh 6800 lbs...maybe your thinking of the Gen1? According to the sticker on my truck and the ford web site the truck weighs 5,525–5,697 lbs depending on SCAB or SCREW.
You claimed that a good weight distribution hitch would be 250lbs...OMG what are you talking about.
https://andersenhitches.com/Product...itch-4-droprise-2-ball-3-4-5--6-brackets.aspx Shipping weight less than 50 lbs.
You're estimates are off by several hundred lbs and contain false information that is not helpful to the OP.
It is true that maxing out the tow rating at 8k lbs will mean you have less left over for passengers/additional cargo.
I also agree with your tongue weight calculation.