First off, slow down. 65mph is a max speed for the tires so keep it in the 55-60 mph range for safety. Exceeding the max speed rating of the tires is inviting a chance for a blowout and they aren't pretty. As far as the bouncing around in the trailer, I assume you have the stabilizers on the ground. You are still on the springs of the trailer so movement will always be there unless you put stabilizers under the frame near the axles. The only way to totally stop the movement is to lift the wheels off of the ground which isn't practical.
2014 Palomino Puma 25RS
2011 F-150 Super Crew XLT
Days camped in 2014 - 23
Camped 2015 - 47
Camped 2016 - 51 done - 6 more planned so far