Finally had my M3 serviced at BMW. They re-balanced the wheels and performed a new alignment to dial everything in.
I took the M3 on the freeway to see the results. The strong vibrations, I'm glad to report, are gone...
I assume there was a combination of issues that caused the bad vibration (wheel balance, alignment, and uneven suspension height).
In regards to the height of the suspension. The M3 was sitting uneven when I initially had the rear suspension dialed in using the collar height. I talked to KW and they told me to adjust the height using the "Wheel Hub to Fender edge" measurement as a guide. When I initially had the suspension dialed in equal on both sides (using the collar measurement) the height was off left vs right. KW told me that some M3s sit different than others so you can't rely blindly on adjusting the suspension height (using the collars as a guide) but instead measure the height from the wheel to the fender.
We adjusted the height until we had an equal distance on both sides. Ground to fender measurement at the rear was 26" at the end.