Steering wheel/tire shimmy over 75 mph. on 2002 Honda Odyssey

Rookie cbe0621eac06868b3efe0d8d1d3611e23c60d3114864ea2ec19a68cfbd3eebab
Hi. I have four fairly new Michelin tires, balanced and rebalanced and rotated at least once since purchase about 2500 miles ago. My minivan steering wheel starts shimmying at 75 mph and above and then stops shimmying when I coast down to below 75 mph. When I brake to slow down on a long downhill grade from speeds above 70 or 75 mph, the steering wheel shimmies again and gets considerably worse, the harder I apply the brakes. Any suggestions or ideas of what the problem may be?
(1) Answer
There could be two to three issues. The first being tire balance. You did say that they were balanced and rebalanced but sometimes the tire balancer will not be as effective over 70 MPH. The second issue is the brake pulsation. I have seen warped rotors cause a vibration at higher speeds. Since you mentioned the shimmy when braking that could be the root cause. The third issue could be an out of round tire or a slipped belt in the tire that wouldn't be picked up with a normal tire balancer. If it were my vehicle I would have the tires balanced with a balancer that compensates for tire surface (hunter makes one) and I would turn the rotors to stop the brake pulsation/shimmy.