Thanks to all you guys' input and I will proceed from here. In my haste to first post maybe I was not real clear. These rounds are hitting where you're holding, within 2" except for the occ. "flyer" which goes awry, not off the paper but definitely not where you were holding when the hammer fell. It is always this "flyer" that does not cut the perfect plug. This is not even close to "tumbling", but is rather a sharp, round hole with just a little lead smear and tearing in one spot.
Yes, targets are always on cardboard backing.
I have and still do run some 158 gr LSWC from places like Tenn. Valley Bullets sized to .358 with good results, and haven't observed any similar problem.
Okay, Smith, I used to burn some BE, and will try your advice.