Why the Shelby spec items? Unless your goal is nostalge, there a much better modern options these days. Better suspensions, better brakes, aftermarket fuel injection, etc..
Honestly, if it were me, I'd drive it as is with minimal mods for safety, and find another for a project to go "Balls to the Walls" with.
Thank God your side trim wasn't those rivit on extruded aluminum channels with the rubber inserts.
Try placing the rear on jack stands and loosen all the spring to body bolts to see if the springs were just bolted on wrong. They might just be under tension from the bolts.
1966 GT Fastback, restoration almost there! Code T Red with White LeMans stripes.
2015 GT Fastback - Deep Impact Blue