It looks like you have run up against the max payload limit which is often the limiting factor.
If your payload limit is 1764 lbs. and your family/cargo load is 1000 lbs. you have 764 lbs. of tongue weight available.
You also have to be careful that the Max towing applies to your model and extras. In my case my F-150 is advertised as 11,000 lbs. towing; however, that was for a select line of vehicles with the super spiffy towing package/motor combo, getting into the details I found that my specific truck options only allow a little more than 9000 lbs. Plus, the real limit was the max cargo of 1411 lbs. posted on the door sticker.
I would guess a 5000 lb. trailer is more in keeping with your vehicle ratings.