Thanks for the reply, circuitsmith. Not what I wanted to hear, but I suppose that could be it.
Regarding the comment about “inherently imbalanced”… That is what the mechanic explained to me. I also read it on Wikipedia:
“Balance shafts are most common in inline four cylinder engines which, due to the asymmetry of their design, have an inherent second order vibration (vibrating at twice the engine RPM) which cannot be eliminated no matter how well the internal components are balanced.”