I know exactly what you're talking about, and you're right to hold off on the tyres for now.
Get yourself a set of adjustable ARBS (Eibach are very good from experience) and then the full set of underbody bracing (IIRC there's two braces at the front, one giant one in the middle and another one at the rear) from GT Spec or Summit. The bracing alone will give you far more feedback and also sharper steering at the front end, whilst the back will give you a tighter rear end for more control when it does break loose. Also a good set of adjustable A-arms on the front suspension and camber arms for the rear will enable a more positive geo to be done on the car, allowing even more fine tuning.
Do that, then do the suspension if you're still not happy. I suspect you will be though, as from your previous posts I can tell you're a man after my own heart where feel from the car is above all else.