The age of the tires is the date they were manufactured, not when they were purchased and mounted on the rims. They could have been on the shelf up to "years" previous before sale. Even tires have a shelf life.
If the car sits for long periods of time raise it up on jack stands so the tires are just off the ground. Make sure they stay inflated.
Another thing to note. Using "air" to inflate tires is OK as long as it is a clean ,dry source of air.
High dew point "Wet Air" (that is air that contains a lot of moisture) when compressed will have that same amount of moisture concentrated in it when used.
If the moisture is not removed from the air before it goes into the tires it will fall out of suspension when the tires cool and "puddle" on the low side of the tire.If it freezes over night there will be ice formed inside the tire on the low side.That will cause an imbalance untill the ice melts.
That is one of the reasons nitrogen fills on tires are preferred. Nitrogen is cleaner , dry (no oil or moisture content) and expands /contracts less than "air".
Believe it or not : wheel trim rings added on after rim/wheel balancing (if not zero balanced themselves) can throw the balance off and cause vibrations to show up at certain speeds.
Avoid using "custom car show " doo dads like dice etc. etc.
for valve stem caps . Those add extra weight to the valve stem .If they were not compensated for when the wheels and tires were initially balanced ?
You guessed it ! OUT OF BALANCE!
Insufficient shock absorber cooling , damping rate or aged shocks can contribute to a high speed vibration.
If the tires have not been flat spotted during a panic stop this is what needs to be done to solve high speed vibration problems.
For sustained highspeed running tires need to be checked for roundness.
If they are mildly out of round they can be 'trued" on a machine that will remove rubber from the highside.
With the tires removed each rim needs to be checked separately for trueness/out of round , lateral runout and zero balance.
Used rims definitely need to be checked before mounting tires on them.
Even "new" sets of rims should be checked this way before ever mounting tires on them.
Each brake drum/rotor needs to be checked for out of round , zero balance and lateral runout.
Rear axel flanges need to be checed for out of round & lateral runout.
Are the axles straight?
Front spindle flanges need to be checked for out of round and lateral runout
Front wheel bearings need to be checked for proper preload & wear.
The drive shaft and U-joints can cause vibration problems.
A worn or improperly installed /binding u-joint can set up a vibration at speed.
Are the driveline angles correct?
Pinion and trans angles may need to be adjusted.
If the original stock driveshaft is still being used get the shaft checked for straightness .If it is a keeper get it highspeed balanced, if not, get a new one made.If a new one gets made use a larger dia. like 3".It will have less tendency to bend or twist.
The original drive shafts from the factory, beginning some time in the mid 1970's, had vibration issues because the factory saved money by not precision balancing them.
GM figured that since the national speed limit was 55 mph most cars would rarely see over that speed .Right around the same time the 80 & 100 MPH speedometers started showing up along with the unleaded fuel only gas gauges.