I personally would expect your tongue weight to be in the 1300-1500 lb range.. there is NO WAY you are going to stay at 9,000 lbs. Not with 2 quads, 2 bikes, Fuel, and camping equipment
6300 lbs dry as you say...
Add propane, your gear for regular camping, clothes, dishes, food, coolers, weight distribution hitch snap up brackets, flashlights, spare bulbs, card games,fire sticks, etc etc etc... an you are quickly at 1000 to 1500 lbs more... that comes to close to 8000 lbs. Then add 850-900 lbs for your quads.. then 400 lbs for your two bikes... well, that puts you at 9,200 lbs.. don't forget your tools and spare parts.. now you are 9,500 lbs.. wait we forgot fuel... 9,600-9,700 lbs...don't forget the grill! or the charcoal!
This is just the process that usually happens.. weight creeps up on these things...
The problem isn't with your proposed trailer.. its with the tow vehicle... there is more than enough tow rating... but not enough receiver rating...not enough payload...not enough rear axle rating.
I'm not trying to be hard on you, but the reality is that your are squarely in 3/4-1 ton range.
Will your current truck blow up and the wheels fall off if you go for it?...no...not immediately.. but eventually... you will wear it out faster... plus when Mr. Murphy pokes his head up coming down that mountain, or at 65mph when a tire blows out... it will not be the time to go get the proper TV.
Thanks and good luck!
Jeremiah