The ride in this car is intentionally made that way "GT" package. the springs will tend to be a little shorter and a lot stiffer than everyday mustang springs, plus a good sway bar front & rear. This creates lower center of gravity, & less body roll during hard cornering, helping to resolve the inherant problem of understeer. if you do change your springs to taller softer springs check for tire clearance at full travel, they may compress to a shorter height than stock GT springs.
Chances are the car has been fitted with lowered springs. Those cars had a silly looking very high ride height, and many people, me included, lowered it to look better. My car had a great ride until I ut those Eibachs on it. I think you can now get progressive rate softer springs (Eibach again) now that will improve the ride greatly. Having said that, If you want a good handling car, then there are tradeoffs or ALL cars would handle like Corvettes.