I am late to the discussion here, but most of my cars are big blocks with the 7 leafs and all have sway bars up front, and their stability is pretty good. But as the cars age, the rear leafs take a setting that is too low in the back for me. Until I restore the cars and add new leafs, I have put in load assist shocks from Monroe (Gabriels do not have sufficient boost, and even the Monroes are not what they used to be, but they are a little better than nothing). I agree with Dave that these cars look best with a little rake to the body and the added stiffness is always welcome to me. I will also be specifying a 1" height increase when I order new springs, and leave out the load assist shocks. But in your case, some load assist shocks may help a little. I also always specify the biggest whitewall tire I can get on a C body (except blackwalls on some cars such as the Sport Fury GT or Hurst), as the load ratings are better and help stability too. So I always get the 235-75-15s when I order tires (and would also consider the 70 series if they were available anymore), to make the handling as good as possible. In my opinion, I would never get tires as small as the 215 series on any C body, way too small in my opinion for good stability. But radials have squishy sidewalls too, that will worsen stability in handling maneuvers compared to bias plies on the older cars, so direct comparisons are difficult when recalling long past memories of the handling of these big cars. I find it interesting that the convertible comments here suggest the bodies are acceptably stiff, as I find they are wiggly and less than stiff such that I am wondering if I even want to do a convertible, as the lack of a good structure turns me off. Plus I don't like being on display with the top down in the Los Angeles area - maybe out in the country I would feel less vulnerable given all the whack jobs in the world these days. I also like tight steering boxes from Steer & gear that have nice precision. Interesting thread.
Steve