Exper,
Gamecock 20's are fairly light upland guns and will kick the oatmeal out of you with big loads. I shot some 1 oz Hi Vel loads out of a similar gun a couple years ago. Not pleasant and probably about the limit of the stock and other parts. I'd not beat up a little gun like yours (and your shoulder) with 3" mags even if the chambers were 3".
Hell, coyotes crumple to a .22 win mag rimfire with solid points out to over 100 yds. In effective shotgun range, say 40 yds max, a 22 mag is in it's prime. A shotgun with shot will not be effective near as far out, and a slug in a smoothbore won't cut the mustard for accuracy out at 100 yds IMO. Coyotes are thin skinned and small animals that don't take much killin, IME.
If a 22 win mag rimfire is allowed, I'd take a scoped one over a smoothbore for coyote hunting anyday.
As for turkeys, I've only hunted them once (last year) and saw a bunch but didn't get in bow range (further than shotgun range, for me). I did bring a shotgun and some #5, 1oz and a full choke. I see those guys that hunt them on TV using huge shot and extreme chokes just to hit them in the head. I've never understood the need for huge shot if they are head shooting them. But then, I've never shot one, let alone disect a turkey's head to see if it was an inch thick of bone. I recommend a 90gr Thunderhead, 3 blade, carbon shaft, 3 fletches of 4", coming off the rest at 260+ fps.
