Welcome aboard! Many of us came from a drag race background and there's a little bit of a learning curve to learn about cornering better, you're in the right place to ask questions.
The biggest question before any of us give you any advice is what exactly do you want to do with the car, and how fast do you want to go through the corners? Knowing that will help fine tune what you'll need to accomplish those goals.
Consider this- pretty much all popular rear suspensions bind at some point. What you've got is a great drag suspension but as you know it's lousy for handling and is really good at binding up in corners. Leaf spring set ups work ok for a cruiser and can even be tweaked a bit for cornering but they also are bind prone and can suffer "axle wrap" where the springs get all out of shape. There isn't much tunability in them either. A triangulated 4 link is a popular upgrade but because you're dealing with different lengths and angles on the arms they bind up surprisingly quick too.
Your front suspension is designed to guide you around the corners and the rear suspension is supposed to follow along without argument. When a rear suspension binds it "shocks" the system and throws the balance off making a quirky and unpredictable ride. It can also unload one of your tires and of course the best way to corner fast is to keep as much rubber possible on the road at all times. Not all suspensions can do this equally.
For a street driver that sees some track time many folks like Speedtech feel a Torque Arm is at the top of the suspension food chain. There are several advantages to a set up like this, in a nutshell they ride very smooth, handle very well, are predictable, and have considerably less bind than the other more traditional suspensions. There's a reason GM went to this system for Camaros and Firebirds in '82 and didn't drop it until they went to independent suspensions on the 5th gens.
Speedtech offers complete front and rear kits for your car, from basic bolt in entry level cruiser parts clear up to our ExtReme kits for those that are serious about hunting trophies. Here are a couple pics and links to products so you can read up a little more.
Notice that with our torque arm you can keep your 9", our kit has braces that help strengthen the rear half of the car, we have Articulink 2-piece trailing arms that rotate to help reduce bind even more, and the strength of the center arm is built into the arm to give you a clean and simple installation with plenty of room for exhaust and such. If you're looking for a little more than just a nice cruiser check our parts out.
Our 2nd gen (70-81) F-Body suspension page- http://www.speedtechperformance.com/...=cat/cat36.htm