[Bear]

I think you have answered some of the question with the shcok/strut issue. Also, the rear sub frame(beer cans) bushings can give you this problem. I would start with new struts (BOGE or Bilstein), and see how that feels. If that does not solve the problem, follow up with the front outer sway bar links and then the rear dog bones. As a last resort the beer cans (they are pricey so wait on those). My son's 1988 735i was a bit squirrly and new front strut inserts as well as the beer cans solved his cars problem. My 1988 750 would tend to wander and new front strut inserts (Bilstein Touring) helped me out.