On the road again has it right in finding a possible tire issue quickly, move the fronts to the back one at a time and see if the problem goes away. A 60 mph vibration is most commonly a balance or radial force variation issue. If you come back to a possible balance issue, have your wheels balanced on a road force variation balancer. The balancer loads the wheel tire assy during balancing to simulate the load placed on it during operation. This will find a fault within the tire a standard balancer cannot. The balancer will give the force variation in pounds. I believe Hunter reccomends less than 36 pounds variation for a light truck and around 25 pounds for a car. I don't know how sensitive your truck is, on front wheel drive cars we shoot for less than 10 pounds to eliminate vibration complaints. A straight axle truck should be OK with much higher numbers.
John