The gun sounds alot like mine (described above). I use an 1150 fps published (Alliant) 1 oz load calling for Green Dot in STS hulls that generates 6300 psi. But I only drop 7/8 oz of shot. Velocity approaches 1200 fps, and is consistent. This load is extremely soft on the shoulder, but I used it a coupla weeks ago to good effect on phez and chukar with #6. Practice loads get #8s. In your situation I would: use the softest shot I could find, and simply add spreader disc or soda straw inserts. Then......pattern test.
Sam