I had the same experience last summer on my 17 Chevy 2500HD Duramax Highcountry. In the old days if tires were slightly out of balance successive turns could cause the shimmy to come and go. Same is true today. It is hard to find sufficiently smooth roads in MT to experiment especially in winter. Mine has had 6 Michelins road forced balanced and still vibrates. It sits in my woodshop all winter hoping for a buy back or enhanced trade in. The notion that weight in the rear helps is one I agree with or at least added load reduces the sensation.
Mine did not vibrate the few times I hit 70mph pulling a 4500lb camping trailer last summer. I usually keep it to 65 when towing.