NO, don't get the wheels re-balanced and rotated first. Your indie may not have adequate experience with this sort of situation. As I said earlier, I went through the same thing. It took a well experienced old mechanic to tell me that the first step was to check the tires and rims and then he found the problem and now I have no vibrations whatsoever.

Tell your indie to put the tire + rim on that balancing machine and then check to see if the wheel is bent and make sure the tire is smooth and round all the way. The reason for that is because even if the bent rim is mounted on, say, on the driver's side of the front axle, when you rotate it and put it at the back, the vibrations will persist, though to a less extent.

Just have your indie check ALL FOUR tires and rims. I bet you that's where your problem lies.

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1999 Mercedes-Benz S600, 103K miles - garage queen
1988 Mercedes-Benz 560SEL, 89K miles - daily driver
2007 Hyundai Sonata Limited, 31K - daily driver