New tires no shakes
I had the same issue with Monsters and replaced the tires with Wilkenson retreads, I have since experienced no vibrations at 30Kts and that was two years ago without rotating the tires or balancing. Monsters are good, but I had a bad set, I believe, the point is, the replacement of tires made it all go away. If nothing else works, try a new set of tires and see if that improves the rollout, if it does, its the tires, if it doesnt, keep the old tires for future replacement and focus on other factors.
As mentioned before "balanced" doesnt mean a nice round tire, and nothing will resolve that, other than skimming the high points.
Best of success!
Let us know what ended up working!