Are you sure the wheels are identical? I think the ET could be different between the front and rear wheels by your description after changing the wheels.
Not much of any help. Shaking could be that one of your wheel could be damaged by example a pothole. Inner barrel of the wheel. But that should show up when you balanced the wheels I guess. It can also be the tires.
Have someone experienced drive the car and see if they can give you a clue what needs to be fixed.
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