As far as I know, if the car has the rear bar it has the handling package already installed. The differences were in tuning to offset engine weight differences, but since both cars had the same engine, both would have the same suspension. The only possible difference would be the front spring rate as GM used a computer to select the springs based on weight. However, spending the time to swap out one set of 28-30 year old springs for another is pointless as both would have taken a set and lost at least some of their original spring rate. To improve handling, I would suggest a new set of springs and new polyurethane bushings, as well as new ball joints and tie rod ends and maybe a steering coupler. I have the Eibach lowering springs in my car, but have come to the conclusion that they are just too stiff, so I would suggest something milder. Also, a swap to at least 16x8 inch wheels and 245 50 16's would do wonders for the handling. These are heavy cars and they tend to completely overwhelm the puny stock tires with their tall sidewalls, handling package or not. 15x7's with 235 60 15's may also help in a pinch, and many 3rd gen F cars came with the Pontiac Rally II wheels in that size stock. Optimally I would use 17x8 front wheels and 17x9.5's in the rear, but I am unsure if they really would fit your particular car or not.
One more thing: The easiest way to check the sway bar size is with an open end wrench. It can basically serve as a caliper to tell you the diameter of the bar. For example, if a 7/8 wrench fits it snugly, you know you have a 7/8 bar.