I saw a similar issue with a Cessna 185. There was some vibration but not an unusual amount, but the owner decided to give prop balancing a try. The technician could not balance the prop because he could not get a steady reading on his equipment.
After much research it was decided that there was likely an internal engine issue. It was also found that one prop blade serial number was different from the other blade but there was no record of any prop work in the logs. Finally there was a "rumor" that the airplanes tail had been blown up in a wind storm with the prop vertical causing one blade to hit the ground and be bent when it was operated by the previous owner.
Bottom line: The engine was torn down and a crack in the front main bearing web was found. It was considered likely that the engine would have eventually suffered a catastrophic in flight failure
