We had the props on our Aztec balanced this summer. The man that did it is
a long time friend of mine that runs an aerial application business (crop
dusting). He and his family have been in it all their lives they are all
CFIs A&P/Is. They own many airplanes and many helicopters. Anyway, they
know what they are talking about. They balance props on round engines, flat
engines, turbines, and blades on both shafts of the helicopters.

The biggest problem he told me that he's had balancing props/engines,
including round engines, is when the engine mounts are worn. Nothing you
do, no amount of weight, will balance a prop attached to an engine that has
bad mounts. Even if you don't think they look worn or burned, they can
loose their rigidity and become spongy. I replaced the mounts on our
right IO540 in less than 3 hours. Mounts from AirSuppliers.com cost me
$270.

Another thing to look for is to see if any weight had been added to the back
side of the ring gear/flywheel. You may be adding weight to the prop that
is counter-acting a weight that has already been added.

YMMV
Jim