I also have one of those Shaw barrels except mine is mounted on a Savage M-10. A max charge of IMR 4166 with the 100 gr Hornady soft points is very accurate in that gun. So is a max charge of H 414 under a 117 gr Hornady round nose. A Sierra 117 gr HP with a max charge of 4166 shoots to the same place as the Hornady RN at 100 yards. The 100 gr Hornady and Sierra loads are from the magazine like 2019 Hodgdon load manual while the 117 gr RN came from the Hornady 10th Edition manual.
I've been trying CFE 223 with the 100 gr Hornady bullet in a Bubba'd Model 99 with no luck. I've even gone over book max a little bit trying to get the velocity up as that seems to be tightening the "patterns" somewhat. That gun shoots 100 gr Remington loads great but nothing else so far.
