I know that you said you don't want to install a higher stall converter, but with the 6R80's stock stall speed, approximately 2000-2200 rpm, the 2011-2014 GTs are definitely lazy coming out of the hole. I have a 2014 automatic with a 3.15 axle. My best 60 foot with drag radials, Steeda CAI, 93 octane tune, and great DA was 1.88, but it's typically 1.9x. The stock NA torque peak is around 4300 RPM. With my 2012 GT (275/60R15 drag radials, MT-82, 3.73 rear end, Steeda 93 octane tune, stock airbox), I can pull a 1.75 60 foot because I can launch at 4300 RPM. I know that the 3.73 helps, but when comparing the manual to the automatic, you also need to compare the 1st gear ratios. As previously stated, first gear the 6R80 is relatively low, 4.17. When you combine that with the 3.15 rear axle, you get about 13.14. With the manual, you have a 3.66 first gear. When you combine that with the 3.73 rear axle, you get about 13.65. So they are not that far apart, based on the stock tire sizes. Of course, a change of tire diameter will also affect the final drive ratios. On the manual, I went from a 27.3 inch (235/50R18) stock diameter to a 28.2 inch drag radial, which allowed me to reduce the final drive ratio (3.61) and stay in 4th gear going through the 1/4-mile trap. On my automatic, the stock tire diameter is 27 inches (Brembo 255/40R19). I chose 285/40R18 drag radials with a diameter of 26.9 inches because I didn't want to reduce the final gear ratio with a taller tire. Although I am still running the stock converter in my automatic, Circle D suggests that a 4C (3800-4000 RPM) converter would shave at least 2 tenths off the 60 foot and perhaps 4 tenths or more off the ET. Given the fact that your car will see mostly track duty, the street manners would be less of a concern. Sorry for the long post, but I thought this information may be helpful. Good luck, regardless of how you choose to modify your car, once you have it. If you are interested in my experience with my 2012 and 2014 GTs:
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