Vibrations at that speed are almost always tire-related.
- out-of-round tires
- out-of-balance tires
- bent wheels
- incorrectly installed / shifting runflats or beadlocks
- using flange-type lug nuts with wheels that need acorn-type nuts
- tire defects (soft spots, etc.)
Steering and suspension components do not cause this problem, but they can make it appear worse. This includes shocks, ball joints, idler arm, pitman arm, tie rod ends, control arm bushings.
There are many other causes of vibration, but they are usually felt at speeds other than 62 - 68 mph. These include drive shafts, diffs, brakes, halfshafts, hubs.
Hunter makes a very nice tire balancer that also measures runout and road force variation. Many Hummer dealers and some larger auto shops have these machines. You can probably contact a local Hunter rep to find someone that has one.
You might also try swapping tires around to see if you can get the problem to move / change. If it will not move, it is probably not related to the tires/wheels.
HMMWVs get the shakes due to old or no longer absorbing shocks at over 40 K miles of moderate offroad use. It doesn't take much to destroy the shocks ala high speed off road use. If every bump feels like a crash, you know your shocks are toast.