Mazda 626 front end vibrates/shakes @ 60 mph

I recently purchased a 1991 Mazda 626. It's automatic with 220,000 miiles.

The front shakes really bad when I hit 60 mph and I can feel it on the steering wheel and the gas pedal when it happens. Below 60 mph the car works and feels just fine, aside from the transmission not engaging 3rd gear sometimes.

The previous owner replaced the front control arms along with the axles, but that didn't do anything to fix the shaking.

Any ideas?