madcat, I think you are going to be asking for trouble with a of drop of that much, for a trailer that heavy and the stock hitch.... Think of that drop as a lever on your hitch and the longer it is, the more stress it's going to apply to the hitch.
A #6500 TT is going to have at least a #700 tongue weight, but probably more. That will usually require a WD hitch setup, even for a F250..
Add even a 10" drop and that #700 tongue weight is going to exert a lot more leverage on the hitch, then say a standard 4" drop would... I'm sorry, I don't have the math background to determine the exact #'s in either case, but I know I can break loose stubborn bolts with a cheater bar a lot easier then without one!
My TT hitch is about 18" off the ground when level. Here is a pic of my WD hitch setup on my stock height F150 4x4. The top of my hitch is about 19" off the ground. I think this WD setup is considered a 6" drop! Well, that's where the lower bolt is at any rate...
But, notice that the ball is just a tad lower then the top of where my hitch is. This makes for a level rig, with it actually being about an inch low in front when the WD bars are in place.
For your case, you will need at least a class 5 receiver that has a 2.5" square receiver and maybe even one of those 'double' receiver setups that you see trucks needing to extend their hitch because they are hauling a huge cab over camper and want to tow their boat or toys with...
Probably still going to have to go 'custom' on it at any rate!
Mitch