It shouldn't drone at all. The G8 GT stock exhaust is the quietest exhaust on any V8 car that I have ever heard. I recommend inspecting the entire exhaust system from the heads to the tail pipe and look for any leaks, holes, loose bolts, bad gaskets. Check if the O2 sensors are screwed in tight, check head exhaust gaskets for leaks. Maybe disconnect the exhaust from the midpipes and inspect that gasket. If your rear exhaust flange gasket was bad other gaskets may also be worn out.
2009 G8 GT
2002 Corvette Z06