I would assume that you moved the wheels front to
rear and the problem was still there.
How many miles on the car?
Have any of the steering components been changed?
If it is a "rotational" problem I would think it would be there all the time and just increase and decrease in intensity with speed.
Have all the wheels been checked for "trueness", meaning are they round and do they have acceptable runout?
Some have had good luck with finding a shop with the Hunter 9XXX series balancers.
Just sort of thinking thru the keyboard.