Well, perception is everything, isn't it? I never thought of a ThirdGen as a "big" car.
Actually, weakend springs can cause bottoming, since the spring rate doesn't change but the height does. Stiffer springs will not soften/smooth the ride to speak of unless the body is bottoming out now. TALLER springs (factory height) are probably the real solution. You can measure the ride height to check your springs for sagging.
It is also possible (likely?) that the isolators at the ends of your coil springs are compressed to the point where they offer no padding. While many people replace the stock rubber isolators with harder urethane or polygraphite impregnated plastics, you may want to use replacement rubber isolators since you are not seeking a firmer ride.
Another factor created by sagging springs is that the track bar (Panhard rod) tends to take more of the load at the lower height, unless it has been adjusted to compensate for th elowered height. This tends to transmit a bit more road feel to the body than the factory intended, and may actually affect rear end tracking.
Also, "heavy duty" shocks are often valved too stiff for reasonable ride. Valve design in a shock is everything. A little free oil flow is good to keep the road "jitters" out of the car, but when teh oil flow starts to go high, the valves need to shut it off quickly. Again, this is where many aftermarket "heavy duty" shocks fail, in that there is only a single or very simple dual rate/valve setting for oil control. Tuneable shocks can help. Variable valve rate shocks like the factory installed are generally the best for all-around driving.
Dive under that "big old car" and start looking.
