try loading your 3" (and 2 1/2") shells to a lower velocity. you can get good patterns with the heavier load with slower than the usual factory "max" loads.
a good shot to use for both the 2 1/2" and 3" shells is #8 1/2, it's an oddball but it meters well, patterns good enough, and works on anything from bobwhites to pheasant up to 15 yards. i can't speak for squirrel, never shot one. my trap shooting buddies turned me on to #8 1/2 shot, they swear by it.
other shot sizes work equally well when loaded to proper velocites, i have used 1/2 oz of #6 shot on pheasant with excellent results, meaning the bird died every time !
in general terms, but not always, patterns that have holes in the center are be caused by poor internal ballistics.
sg