Keep in mind that loudness of your exhaust does not mean more vibration. Vibration can be a function of frequency. If your current exhaust is quieter but has a more bass-y sound, then the may be the culprit. It may even be a super low frequency that you can't even hear. My bet is this is the issue.
If the exhaust is ruled out, then I would inspect the engine mounts, gearbox mounts, and differential bushings for bolt torque or failure.
The E90 M3 is new to me, but I believe the gearbox is bolted to a subframe. If there is a subframe, then check each of those bolts as well, including whether a bolt is missing.