I've seen virtually stock 99-04 GT's hit low 13's but they were being ultra aggressive in their driving, had better rear suspension, adjustable shocks and struts, and slicks. Everyone gets hung up on the horsepower number but reality is to run 13s takes 270-280 hp. 12's taked 330 hp and 11's takes only 400. It's getting the power to the ground that counts.
Get some slicks, adjustable shocks and struts, better control arms, and learn how to drag the car. Most of all, get the
tranny set up properly which means for a stick, get a suitable clutch, aluminum flywheel, shifter and driveshaft. Automatics need a shift kit/valve body, higher stall converter, rebuilt with high performance clutches and bands.