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 !