So your rear axle is supposed to weigh no more than 9600lbs. GVWR is 14500. And GCWR is 22,000lbs. So in my case, my Rear axle is at 9000 lbs. Remember, keeping extra air in your air bags, I run at 70 psi, raises the rear up and puts more weight on the front axle. The Coach overall is at 13,500 lbs fully gassed and loaded.
My toad is 4860 lbs. some would say you are too close to the limits with my toad but remember there is an incredible safety factor in those hitches. They are very conservatively rated and also remember the carrying capacity on a normal truck hitch is nearly double with a weight distributing hitch.
I know a guy who has been towing over 7000 lbs for years with a 3500 lb hitch. Found him on the forest river forum.
The 350 lbs may be weight on the bumper itself. I've hear those bumpers are not rated to carry much weight and 350 strikes me as what mine is. Check it out to be sure.
Overall they have not told you anything wrong. You just have to know your weights and the advice on the hitch is good. That's why folks tow with a dolly or 4 down. Either of those options put very little downforce on the hitch itself.