A bad tie rod WILL NOT cause shaking between 50-80mph. ONLY a bent/out of balance rim will cause that. A bad tie rod will cause the car to have bad steering response and make the car NOT go straight. anyways did you ask him if it is the inner or the outer tie rod, that is bad? It could be either or both. If your need new ones, A guy on ebay sells sets(both inner,outer) for around $50/pair shipped. local auto parts stores are going to charge you around $50 for each inner and each outer.($200)

 

Heres your list to check.

RIMS ! Tires ! THAT IS ALL

Tie rods will not cause vibration just bad steering, sloppy steering.

Wheel bearing will make a noise if its bad. You WONT miss that one.

The Back and forth movement test is a crock. I did that to customers all day OH look mam your tie rods are bad look at the play i get !

Check all your joints and try a different set of tires and wheels.

Motor Mount wont cause this at different speeds. It would vibrate constantly and change at RPM.

Since you have a speed diference in effect its your rotating assymbles ie WHEELS AND TIRES ! have you had JUST the rims balance ? prolly not I bet that RIm is more bent than you think !