My question is, what might cause an unusually shaky, bumpy freeway ride at speeds of 70-80 MPH other than tires being out of balance ?
They were last balanced 7k/ 6 months ago.
Car is 87 Accord with 184k
If the struts are worn, the tires can begin to bounce up and down as the vehicle is driven. This is called wheel hop. Check the tires for evidence of cupping. If a tire is found with a cupping condition, that strut is worn.
Tester
You can also get this from worn out tie rod ends, worn out ball joints, and some other possibilities. With a car this age it’s a good idea to get it into a good shop and up on the lift.
Also, just to add, an old tire with a separated chord will be sorely out of balance. Sometimes, it will only be evident at high speed or on a balancing machine. A tire can get out of balance in 6 months, easily.
Have you checked the tyre pressure?