I confirmed later that day that Grizzlies from a flatband slingshot WILL kill pigeons.
I don't know how I missed the thread Manny put up about the Winchester not liking the Grizzlies. I ended up ordering a tin and holy moly...I'd be lucky if 1 in 3 shots actually hit a 12x12 target box. For anyone with a .357 Winchester, proceed with caution when using slugs. Mine does not like slugs at all. She sure loves her JSBs, though.