Regular balance and tire rotation will help with tire wear, but not necessarily help with vibration issues.
Do you know exactly how old the tires are? Not just when they were installed, but by their manufacture date. Look for the DOT stamp. If the tire was made after 2000, it will have a 4-digit numeric code at the end of the DOT serial. If made prior to 2000, it will be a 3-digit numeric code.
ex.
After 2000:
DOT ABCD EFGH 1204
Where - "1204" breaks down manufactured in the 12th week in the year 2004
Before 2000:
DOT ABCD EFGH 128
Where - "128" breaks down manufactured in the 12th week in the year 1998
If the tire is more than 10 years old, no matter how much tread there is or how it looks, scrap the tire - it is literally a ticking time bomb. When they get to 4-5 years old, even with a good amount of tread, they can develop a significant vibration issue. Personally, I would not run a tire that is 6 years old from the DOT stamp. As you can't tell if the tire is good or bad just by inspecting it - you have to cut it apart, destroying the tire, to know for sure.
At this point, possible that your only alternative is to replace the tires, to "cure" the vibration issues. Tire balance may help with the high speed vibration, but it is only a matter of time before even that will not help.