Getting a sub-5 second 0-60 should not require any mods, no tune, no gears, nada. The 2013 GT with auto should be good for about 4.7s.
To the OP, what size/brand/model tires do you have? Also, as others have stated, the track app might not be accurate. Have someone time you with a stop watch. One more thing, are you testing on a good surface? Is it fresh black asphalt with no traction?
I'm still on the factory Pirelli P-Zeros. Haven't really had much of a problem of losing traction with them though, I can generally stomp it and it only spins a bit even with all assists turned off (which strikes me as odd, I have lesser powered cars that will rip the tires off if I just stomp it from a dig but they're all FWD). Pavement has been decent that I've tried it on, no crappy beat up pavement or anything just smooth roads. Not freshly paved, but still smooth and pretty consistent.