Your springs MAY have too high a rate, same as my Neuspeeds. I believe they may have been intended for a heavier engine like the V8 or perhaps the 3.2L M104 - I don't know for sure. I would think my 6-cyl diesel would be heavy enough to make the front squat, but it wasn't!
KONI's are cool because they are adjustable (within a certain amount). I'm honestly not 100% sure how they would compare to the Bilstein Sports. I'd try to find a phone number for the KONI importer and ask their tech department. Otherwise you'll be spending money on an experiment. I had a set and I liked them, they also have a lifetime warranty. The struts are externally adjustable over a 2.5 turn range, the rear shocks are a 3-position click type and you have to remove them to adjust. I sold the car that had those (also had H&R springs).
From what Neil V says, if you want a decent ride quality, I'd get a set of factory 500E springs. They should be ~$250 a set from *************** or FastLane. It's really hard to say... if you buy Eibachs or H&R, they might be what you have now, and end up with the same problem. The other OE choice is Sportline springs, but they are really firm. But if you got Sportline springs with Sportline dampers, that would be a factory matched set and wouldn't bounce (ok, *shouldn't* bounce.)
My one car has a matched set of Carat springs with matching Carat dampers. It rides quite well but is a bit soft for max performance. The rates seem well matched, no funny bouncing. My other car has Neuspeeds with Bilstiens (not Sport) and it rides very stiff (due to the springs) and the Bilstiens don't seem to be well matched to them... not enough rebound damping, IMO. For now I'm living with it. I may try the 500E springs, possibly with 500E front struts (which are ~3 inches shorter than any other 124 strut I've seen, and also have internal springs that stiffen up as you "push" the car harder). I can't use 500E shocks because they are self-leveling and my car doesn't have that. So I'm not sure what to try in the rear. Hmmm....
I hope I haven't just confused you more with all this!
Regards,