The problem was how I was using the sling
Somewhere on M4C, maybe someone's tagline, says, "over 90% of the questions posted on gun related forums could be answered with a trip to the gun range." Well, this problem needed both feedback here and a trip to the range.
I was using the sling to stabilize the rifle, and learned that it's just not necessary. apparently, with the FSP at the end of a 12" FF tube, the force I was applying to the tube through the sling was enough to make well-aimed shot groups 3.5" at 50 yards.
Today, I removed the sling and shot 3" groups at 100 yards. Not as good as it should be, but there's still the "loose nut behing the buttstock" factor :)
Good technique was important. go figure.