If the handbrake was stuck on, then you should feel a vibration before you get to 65mph, and the care would be slow to accelerate.

When you felt this violent vibration, was it in the steering wheel or in the seat? This will help to distinguish between front and rear.
It almost sounds like a caliper is seizing cause it takes a while for the vibration to occur.

 

When I was driving, the handbrake was turned off.

 

It sounds like you took off the parking brake, but one or both sides of the parking brake were still applied.
Given the short time span it took the vibration to appear, this would coincide with the time it takes the rotors to heat up from the parking brake dragging.

When this happens again, stop the vehicle and go to the rear wheels. If one wheel feels extremely hot, or hotter than the other side, then that is the parking brake that is seizing...or even a brake caliper seizing.
Look at the surface of the rotor too for any discoloration (like blue or purple).
If the steering wheel was vibrating then the issue is most likely not at the front of the vehicle...it's at the rear.

 

I'll see what happens.

 

No to negate the process you're tying to make finding the vibration, but that noise you hear when running the wheels off the ground is from the diff...because the wheels are not on the ground, it's perfectly normal.
If you were getting that same noise with the wheels on the ground, then the diff is toast.
That's why you never heard the noise before when driving.

 

I must ask you for advice again.

 

What is the brand and model of the tires you have on the car right now?
What is the DOT number on the tires? This tells the production date of the tires.

 

Do you think the tires are the problem?

 

At the end of the DOT number there is a 4 digit number...it will only be on one side of the tire after the DOT number.
For example "2715" would be Week 27 of the year 2015.
If you replaced the tires in 2019, then that set should hopefully have been made in 2019, or later 2018.

When driving a vehicle on the hoist with the wheels hanging, getting odd vibrations and noises is normal.
The issue is it would be hard to tell what is normal and what is the problem the vehicle is having.
You could be feeling the vibration that is causing your issue, or some random vibration caused by driving the vehicle on the hoist...it would be hard to distinguish which is which, and even if you could, how do you find what's causing it.

The way you described the issue is similar to when you park a vehicle for an extended period of time and them drive it.
When parked for long enough, tires can develop a flat spot on one side, the side on the ground. When you start driving it will cause a vibration until the tire rubber warms up and the tire starts to become round again...then the vibration should disappear.

 

Old tires: 3715
New tires: 1019

 

Another set of wheels should be able to eliminate if it's a tire or rim issue.
Since you've mentioned the vibration comes from the body and seat, then it points to the rear of the vehicle.

Without feeling the vibration it's really hard to tell what it could be.
Maybe the tires are just not the best tires, and the vibration is normal for them.

 

Did you manage to solve the vibration issue in the end?

 

Hey man i am having the exact issue in my 07 is250 i have checked and replaced damn near everything please let me know if you solved this issues and if so how All your symptons are allmost identical to mine and i am at the verge of going nuts. Hahah

i am a mechanic by trade and this one has got me stumped !! .

 

me tooooo I got the same problem.

 

what are your symptoms and what year is your IS