I hear you...my last car was a BBP '12. I wasn't going to sacrifice all the performance bits to get the auto and no select shift. My '14 rules that way.
Well, if you think it's exhaust, time to get under there and start looking for witness marks. When you clutch in the engine and trans
do move slightly on their mounts and that'll slightly move the exhaust. Common tap points are the over axle pipe on the DS hitting the panhard support, The H pipe clamps hitting the floor due to being in upside down. Just go in sytematically. If you don't have a lift or jackstands, go to a jiffy lube and ask them to let you in the pit to look around. They might let you, especially if you change the oil while you're at it.
2014 Premium GT, SGM, Brembo, Auto, Tech, Comfort, etc. GT500s, Steeda UCA, VMP auto tune, 100 shot on BBR tune, best et: 11.38 at 120.85
2012 GT, Candy Red, Brembo, 3.73, Tech, Comfort, etc. Procal tune, Roush upper, UMI LCAs, Steeda red bracket, GT500s, 28X10X16 Hoosier slicks, best et: 11.91 at 115.23 RIP