Is all up weight of 9500 lbs. too much for Tundra 5.7L?

Of you have to "crank down on both sway bars" to prevent away, you do not have a safe combination. A trailer should never sway under normal conditions. Sway control is there to maintain control under adverse conditions. I had to pull my 14,000 pound weekend warrior 1500 miles without weight distribution because the hitch head broke. It never swayed. When I bought the trailer, I didn't even bother withe the WD hitch until after I put it through the paces just on the ball (back roads, no traffic of course)