Your quest is similar to mine, the only difference being that I may be further along in my journey toward handling nirvana.
The first thing I did to resolve my similar impressions about my stock handling characteristics was to put Bilstein B6 dampers all around but leave everything else the same. That model B6 was designed for the stock springs. (It actually raised the car slightly I think, although since I didn't measure, that is a sense). I was very satisfied with the expensive results. That is, until I drove a car with the sports package. I guess that's why dealers always have you test drive the loaded models.
So now I am doing my typical endless agonizing over what exact parts I should swap out, and I have been leaning toward an all BMW parts upgrade (BMW Performance Suspension Kit and E9X M3 Suspension Component Kit) with still some lingering doubts about whether the BMW parts (e.g., springs, dampers, sways) will be what I want. But the lingering doubts were drifting away in a confusing haze of analysis until that darn CSSNMS posted his comment "but even then the springs are not quite stiff enough". Darn you, CSSNMS (just kidding). Now he has thrown a small monkey wrench into my belabored thinking and I will have to drive CSSNMS' car to judge for myself.
Although our goals are probably different in many ways, my history of car driving since 1962, including 5 blissful years on the German autobahns and back roads, has conditioned my senses to want that undefinable sense that the car can comfortably cruise at 100+ speeds for hours on end on varying autobahn conditions without wallowing like an ocean liner, and then take the nearest ausfahrt and race around corners with little to no body roll and loss of contact with the tarmac. All without costing an arm and a leg.