I agree with Spuriosity, 2-3/4" 7.5 will get er done.
I'm getting 150s-160s at 30yds in the 10" with 7/8oz of NP #7s at 1120fps. 6s averaged 113. Those are handloads, so not much help in your situation.
OTOH, I fired a 2-3/4" 1-1/8oz #7.5 Kent dove load at paper a couple years back with one of my turkey rigs for the heck of it. At 30yds it ate up the target, real nice and even pattern with way more than enough in the kill zone to seal the deal.
I'd suggest to buy a box of 1-1/8oz 7.5s and see what she'll do.