My brother had a similar experience in his Extra 300. It turned out that
the throttle cable making contact with the cowl. Any part that is rigidly
attached to the engine will tranmit vibration to the airframe. In his
case, the problem would come and go depending on power settings and flight
regimes. At high power, the engine would torque on its mounts, bringing
the cable in light contact with cowl. That was all it took to transmit
lots of noise and vibration to the airframe.

Look for any rub marks inside the cowl, especially around the baffling.
Trim as needed to provide clearance. The engine can move quite a bit, so
have at least 1" clearance.

-Adam Molny