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Measure from the corners of the bumper to the ground on both sides. Then have someone sit on the cornors (one at a time) and measure again. If it is lower on the side then it is blown.
You're going to naturally torque to the passenger side on launch. Could be a spring going soft after to many launches? The shock isn't going to stop compression, just slow it down.
My buddy had the same kinda problem where he would rub when going over bumps and taking off from a stop. We changed out the shocks first because they were only $14 a piece and it solved his problem. This was on a 95 GT but it is still the same suspension.