Your wheel hubs can be bent.
Often there's crap between the hub and rotor, or between the rotor and
wheel which cause the wheel to not be mounted straight.  Try removing
the rotor and cleaning all 4 mating surfaces.
Axles could be bent.
Any worn suspension parts can amplify normal tiny variations in parts
that are normally damped out.  Check tie rods and ball joints etc.
Tires can be out of round, especially toward the end of their life.  I
put a new set of Toyo tires on my fathers V70 about a month ago that
were the most perfectly round set of new tires that I've ever seen - so
good I'm thinking I'm going to buy them just for that reason!

Doug:

Why don't you swap the fron tires side to side?  That tell you if its due to
a tire or suspension.  Also, swap tires end to end.

RCB

New tires or worn.   Machine balanced or on-car.  It still shakes
heavily at above 60 MPH.

Earlier this week I jacked up each front corner and spun the wheel
under engine power and noted that the left side vibrated MUCH more
than the right. at 30-40 MPH (60-80 wheel speed).

I took it to the local Butler tire dealer for a rebalance (They had
done a high speed on-car balance a few months ago, and it didn't help)
After they tried to sell me a new set of fronts (about 1/8" above the
wear bars), they balanced them "the best  they could"

Still shakes just as bad,  Garage testing reveals a change though.
The right side has the most imbalance now.

Is it possible that there's somethign wrong with the car, or do I need
to find a new tire shop?

I was thinking my ipd sport suspension (springs, bars, shocks) might
have a resonance at certain road speeds, but with the front jacked up,
the shocks are topped out and the suspension components aren't working
at all..   I'm wondering if the car is posessed..

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