Harsh ride

Have you tried the shock strut tower bushings...especially the rear. I used to replace mine every 30K miles or so. The strut tower is a weak link in the design as it absorbs much of the stress on this otherwise excellent suspension. Reinforcements in the shock attachment points help, and I replaced with competition (neoprene??) bushings and competition steel reinforcements but I have heard using the bushings from the convertible also helps. My experience is with an E36 however. The sound resembles a shock w/o fluid however...a combination of a thunk/rattle noise especially over small intense bumps i.e. poor Ohio road surfaces. Try Parts Geeks, Pelican Parts, or Google "rear suspension replacements BMW 3 series" and see what shows up. Good luck...that noise drove me nuts for years. It was a simple inexpensive fix. I also installed reinforcements at the top of the rear shock mounts as they can stress out over time, requiring a welded reinforcement ($$$$).

tyres would be my first guess, run flats seem like a good idea but are always a hard ride, have it put on a ramp and see if anything is up but if not its the tyres, p6000s are a good choice, but lower arm bushes go alot on BMs but looking on a ramp it will show you if thats the problem

Andy has a very good point. Run-flats are harsh by nature and magnify ANY ride-related problems...and probably decrease usable shock/strut life. I recently put 50 series Conti Extreme Contac DWS on mine and am impressed the ride/handling combination. Treadwear rating of 540 is also a plus. I live in NE Ohio so light snow traction is appreciated until the big snows come, the I would recommend Nokians as they are aggressive and speed rated.

stay farrrr away from run flats, go with a toyo proxy 205/55 r** it will improve ride comfort dramatically, another thing you could do is replace the shocks and have someone look at the springs on the car and make sure there not cracked/broken