Didn't know it was called hunter balanced.
I did see the machine they used to get the tire up to speed. It looked like it was from the 1940's!
If you are patient, you could buy the stick on weights and do it your self. I balance rotors on our 1000 hp high speed wood grinders basically the same way. Get it up to speed, see how bad it vibrates. Add weight in a random location and see if it gets better or worse. Make a note and add weight or subtract weight. You could probably get it done with about a tank full of gas!!
On my car, it ended up being only the drivers side front. They ended up with weights to the far inside, and a couple of ounces in between the webs only in one spot.
Like Rick said, it can be any part of the rotating parts. I new it was the tire, since mine was fine before the new set.
Scott
PS: I'm sure you won't find a regular tire shop to do this. The place I took my car was a place for high performance cars and race track set ups.