x2 on the shocks. I had that problem on my '62 Suburban. It'd shake at a certain MPH, and if I depressed the clutch, it went away. After checking everything else, I finally checked the shocks--when I pulled them out, I could completely compress them by hand and they didn't rebound! At all. Stayed that way until I took them to the scrap yard months later.
I've also had the issue come up again...not any particular speeds, and not bad, just a vibration. Tires were worn.
New tires, snugged the front wheel bearings up one slot on the castle nut, and lubed the front suspension. 900 miles to Floriduh the next day, and it honked down the highway at 90mph effortlessly. And smoothly.
-Brad