We just had a similar one, but it was a narrower range--say, 40-55 mph. One of the tie rod ends was bad. Jack up the car at the body point, and grab the wheel at the 3 and 9 o'clock locations. Yank back and forth. There should be no play--or if there is, the inner tie rod should move as one with the wheel. Mine had slop. Easy fix. And yes, I'd checked at the last service that called for it--our potholed road must've gotten to it.
If you push up under the wheel with a hunk of pipe, it's the same test (up and down) for ball joints.
If you push up under the wheel with a hunk of pipe, it's the same test (up and down) for ball joints.