Perhaps 6.5 shot would be the optimum payload in a .410 for game, only nobody loads it as yet.
I don't think I'd favor 6 1/2 over 7 1/2 or 8 for doves and quail. That's the largest game birds for which I typically use a .410. 7 1/2 to 8 1/2 works great at the distances I limit my gamebird shooting to. If I were to use a .410 on larger birds I'd certainly like to try some 6 1/2s, if they could be found.
My favorite load as of now is a handloaded .73 oz. payload of nickel plated 8.5s, in a roll crimped 3" Cheddite hull, at about 1150 fps. It's a sledgehammer.