I tow a 12,000 lb boat (900 lb or more tongue weight) with the factory hitch with no trouble. I've towed the boat close to 30,000 miles, and my 19 foot Prowler TT maybe 20,000 miles.
My truck has the "camper group" heavier rear springs, and Rancho adjustable shocks, so it's pretty stable. Even with the boat trailer it squats only about 2". I pump my rear tires to 80lb when towing the boat, and 75lb when towing the TT. I make sure the trailer tires are pumped to their max.
I don't carry the load distributing bars that came with my TT - can't tell any difference when they're there or not there (but my TT is smaller than yours).
I have considered adding a load distributing hitch to the boat trailer rig, but it's not so easy to do with a salt water setup (I figured I'd have lots of rust).
My factory hitch was replaced/upgraded in the hitch recall a few years back - the 1998 original had developed a crack. I check the replacement hitch thoroughly before every towing trip, but it seems to be no problem. From reading TDR posts I thought I might need to replace the factory hitch with a Reese or Titan or some other heavier setup, but so far no apparent need to do so.