Safety will be my top concern. I have to little girls. And the safety of public as well.
This is the Canadian airstream dealer.
http://www.canamrv.ca/~canamrvc/towing/car-videos/intrepid-towing-airstream/
as you can see, they are using a Dodge Intrepid and Chrysler 300C to pull a huge airstream and doing emergency lane change test at 74km/h. Judging from 3 rows of wheels on the airstream, it's got to be 30' or longer.
LR4 has 4090lb max rear axle load. With vehicle curb weight being 5659lb plus 4 passengers and some cargo (~550lb total) and 49.1/50.9 front and rear weight ratio, my calculation shows about 3200lb will be placed on the rear and that leaves about 920lb and I think that's enough to support 800lb tongue weight even without the weight distribution hitch. With weight distribution hitch, some of 800lb weight will be transferred to front axle so that leaves more room for rear axle to handle. So with correct hitch, even 900lb tongue weight shouldn't be an issue.
I compared LR4's curb weight, axle load, max GVW and torque to some of full size SUV and pickup trucks that have higher towing capacity and LR4's spec is quite comparable or even better. I think LR4's 7700lb towing capacity is conservative and limited to it's unique removable hitch design which is more for convenience then durability. Instead of it's factory bumper mounted hitch design, correctly reinforced frame mounted aftermarket design should be more then enough to handle 8000lb/800tw easy.