Strong vibration when at highway speeds

With the mileage on the vehicle the motor mounts and the transmission mount are the most likely problem.
With the mileage you have it is very unlikely the motor mounts are okay, they are probably completely without any rubber in them. This can cause a lot of damage with the excessive engine movement also comes mis-alignment of the engine and tranny which will wear out parts like the axles, cables, etc. Very quickly.
The other possible source of the symptom you describe has been eliminated by servicing the suspension/tires.
The motor and transmission mounts must be replaced as a complete set at the same time. If you replace one or two, they will bear to much of the load and as soon as one fails the other will fail almost immediately from carrying the entire load.
There should be 3 or 4 motor mounts and 1 transmission mount. Sometimes the transmission mount holds the engine and that is why there are only 3 in some cases. Just make sure you get them all and do them all at the same time.