Man this is exactly what mine was doing with my other tires. Vibration between 60-70 only. I knew they threw a weight but they still did it after I rebalanced them. I know you put a different set of wheels on it and it did the same thing, so thats prolly not it. But it is just really weird. My tires that were doing it, only had 10k miles on them, I replaced them and it was gonzo.