What would be the next step after tires, lowering springs and front and rear rollbars for improving the handling of a daily-driver TII? I know polyurethane bushings all throughout the car would help firm things up, but how much is that going to harshen the ride?

 

DAMPERS! Otherwise known as shocks and struts. After tires they're THE most important part of the handling/grip equation.

Get yourself some good shocks, Koni Yellows are about the best off the shelf OEM type adjustable shocks (ie non-intergrated coilover shocks). If you need something a little cheaper then KYB AGX's are a good deal, but the Konis are better. Depending on the stiffness of the springs some non-adjustable shocks might be capable of handling them. Bilsteins are very good shocks, better than Konis, but aren't adjustable. These would be my choice in a non-adjustable, but they're more expensive than the other options.