Your steering shakes may be caused by ply separation, shifting, or
breakdown in your tires. If a ply has shifted it can cause some annoying
sensations at different speeds. These defects will not show up during
balancing. Also a tire could become slightly out of round.
You didn't say how old the tires are but this could happen even early in a
tire's life. You could try swapping the front wheels for the back ones (put
the back right on the front rignt, back left on front left) to see if it
makes any difference. If this cures it you'll have to replace the bad
tires.
Cheers,
Steve C.