That's going to take a little investigative work on your end...
Does the "vibration" arrive to you from the steering wheel or felt from the whole car?
Tires are suspect as they are rated for a specific speed rating - since you're going 65 and ABOVE then the issue becomes more of tire safety and unbalanced problems and the damage it can cause or tires with broken (refer to radial wires) tread or belts - you're getting close to the rotation speed these effects tend to take place.
The rubber, otherwise under no load or less loading - would not have been stretched to form this.
Might need someone's help to spot either loose grille parts or a popped trim piece - but it may help to have someone tag along with you watching your car and what is occurring underneath - even filming it - to help demonstrate the events of that shudder or vibration on the exterior as they drive alongside looking viewing details to help you solve this.
But this doesn't discount the other areas of concern like driveline, sound insulation and even heat shield coming off the tailpipe - again goes by sounds and by how the vibration arrives to you - thru the seat or by the wheel or if gentle braking can help localize this to something like a rear wheel bearing and the wheel cylinder (drum brake) of it picking up a shudder from the lobbing from one of the rear hub worn under extra load due to the shift of weight to the rear and affects vehicles center of gravity and control.
Just some examples.
Others would include...and are considered rarer...
Engine mounts - high speed travel places the entire vehicle in a "wind whack" condition - where the driveline has to pull/push the car thru the headwind and the subsequent drag places the driveline in a condition of torque where an older engine mount can start to vibrate due to a harmonic effect of the tire / driveline rotation and the rotation of the engine vibration at that given RPM for a long period of time - an effect called resonance can make engines that would otherwise spin/rotate normally thru the axis - begin to generate another "fundamental" of the rotation as a very low frequency rumble.
- There was a statement from older owner's manuals of cars from years back, recommended that during the break in process of using the vehicle for short trips and restrict or reduce the use of the car for use on long trips - try to make them shorter trips with more frequent stops. This helps the engine "seat" the seals and allow for better oil control for longer engine life. It was due to issues like Resonance as well as Thermal and Compression issues that can arise from hot-spotting and warpage which can shorten the service life a motor can provide
To get back to the rails...
That is partly due to an older engine mount wearing out - that can also be noticed when you accelerate; that hard the pull of the steering wheel can indicate the weakening of the otherwise pretty stiff mounts shifting the torque and you feel it as a pull in one direction or another in the steering wheel or one wheel breaks traction more often than the other because of this same effect.
Injector and or fuel issues...rarer these days but still possible...
A bad injector or a cracked spark plug insulator - can force an engine mis-fire - but would also set a check engine light due to the mixture change the O2 sensors would notice and you'd feel a lack of power - you didn't describe this so kind of want to mention it but it doesn't mean it's the cause - but poor grades or fuel, leaking vacuum hoses or a plugged air filter also contribute to this condition as making the engine run rough "starving" for air - but you'd smell and hear noises from the engine as it sputters.
Tire pressure or dragging brakes, tend to make the steering wheel reflect the "bad side" by noticing the drag the bad tire or poor suspension issue makes - and follow towards it making you want to correct to keep the vehicle running straight. You didn't mention any sort of pull in driving and lack or loss of control when the vibration occurs - which if the loss or lack of control in keeping the car straight on the road - would indicate suspension issues for it can't keep the sneakers on the floor to run down the track.
Running out of options - but;
"This list is incomplete and will be supplemented as necessary." - I found that in some contract somewhere a long time ago, thought it would also apply to this problem...
