I shoot fall turkeys mostly flying. The way we shoot fall turkeys here is much like how you hunt pheasants. Blockers and flushers. Gotta aim for the head of a flying turkey, thus the 2 3/4" 71/2s, and those hot copper plated loads are worth every penny.
I used to turkey hunt with a 10ga. I still own it, and still use it for the late goose season. It doesn't make a good turkey gun because of it's weight. If you only have an 80 acre farm to hunt it might not matter. If you're going to cover ground, you don't want my 10ga.
I don't necessarly think you shouldn't pattern your gun. I think it's over-rated. Based on guiding turkey hunters and being a turkey hunter, I can say that 99% of the hunters I've been around that spent a bunch of time patterning would have been well served to spend that time scouting. Scouting kills more turkeys than calling, patterning, and camo added together.
Now if patterning is something you do for fun, go for it. If you want to study your shot density down to the nth degree, fine. No problem with me, but I fundamentally believe that time could be spent in ways that will produce more dead turkeys.