Unfortunately if you need sport mode without the pops and bangs you'll need to replace your exhaust. The exhaust that you have right now is the louder OEM upgrade option from AMG. I can't remember exactly what AMG calls the different exhaust options (sport vs. performance maybe) but there is a quieter version available from the factory if you'd prefer to keep things OEM. Maybe another owner looking for more noise would be willing to swap with you.
The noise is created from little bit o fuel getting past the open exhaust valves. This is done by the ECU adjusting the timing. It is 'anti lag' mechanism to maintain exhaust turbine speed reducing lag into next gear and for sounds. I like a little bit.. not a fan of lots or flames.I thought that the noise is a result of a small amount of fuel added, I assume, on the exhaust side. Does anyone know if that is the case?