I've had the same problem after going to oversize tires on my 2500. I went from a 275 70 18 to a 295 70 18 on my stock rims. I had vibration issues at speeds above 62mph. They road forced the tires and it went away for awhile, but came back a few weeks later. There were so many weights that on some of the wheels it was hard to tell if some fell off. I don't off road with it.
The tire manager (Big chain tire store) ordered a few more tires and got the weights reduced, but some vibration remained. I ordered a set of Centramatic tire balancers and the vibration was gone. Rode smooth, just like it did with the factory tires and the 2.5" front lift.
After 1 year the tires were rotated (and rebalanced) the vibration started again. They kept blaming it on me and the truck. The first time the truck had 17k on the odometer and I had it in for an alignment cause I removed the front lift kit. Nothing was found to be worn out, needing replacement.
The big chain tire manger unloaded on me how he spent all this money replacing some of the tires and it was only me complaining about vibration. He said my tire/wheel combo weighed over 100#s and I'd just have to live with it! I offered to take him down the interstate so he could experience the issue, he declined.
Since I had an upcoming oil change and they also had a road force balancer I'd let my dealership have a go at it. The dealership said that some of the tires were way off and one of them would not road force out, but when the tech took it down the highway the vibration was reduced from his initial test drive.
Now the Centramatic road balancers for the Heavy Duty only balance up to 6 oz and does not solve for every problem the tire/rim combo may have. (Quoted to me from the manufacturer.)
The wife agreed the truck rode much better on our 750 mile road trip. The dealership tech mentioned it could be the rim or the tire. I bought a slightly used factory rim off of Used Carparts.com and brought the truck back to my dealer to have another crack at the balance. Another $50 and the balance was better, but still not in spec. When I went home I noticed my water bottle stopped vibrating on the center cup holder by the floor. It was the right side (front) tire/wheel that was giving us the vibration.
My take it is the tire and not the rim! Nothing to do with the leveling kit! I can live with the small amount of vibration I have and I'll never go back to the big box store where they either don't know how to use the road force machine, or don't care if the tires are stacked with half a dozen weights on each rim! I got another year, maybe 2 left on these tires and I may change the brand as well! Currently I have the Cooper XLT3's.
I will not go back to the stock size as I like the look of a bigger tire filling up the fender well opening and the added traction of the AT tire along with the extra ribbed sidewall to protect it when I get too close to the curve when navigating my way around a busy/small intersection in the city since the heavy duty doesn't turn on a dime. I tow a 5th wheel camper and sometimes I get on soft gravel, or mud and the wider tire is a plus too! Yeah, I'm down a little gas mileage wise, but it's not all about gas mileage. I still get 16.5 on the road at 75mph without the camper.
Good luck getting it sorted out!