We'll get you back in the game and you are correct that your pattern is lacking. Do you have the means to post a pic of your 30 yard target?
Should be able to tell if your choke constriction is too tight / too open in this way.
If all else fails and you like the .665, (which by the way is pretty much the go to turkey choke for most manufactures), I would buy a box of Remington Hevi-shot #6.
They aren't as impressive as the Nitro Hevi's, but they certainly have out patterned anything else I've shot in the last 6 years. By comparison, the Remingtion Hevi's are half of what the Nitro Hevi's cost.
The Remington Hevi-shot #6, out of three different shotguns I've tested, (using chokes that ranged from .660 to .670, with a .660 and .665 doing best), would stop any turkey at 40+ yards. I don't wish to shoot in excess of 40, but I know that these loads could do so reliably.
In defense of the Nitro load, I have never seen a pattern as good as what the Rhino choke throws with Nitros. Go over to
www.nitrocompany.com and see for yourself. It's all in what you want to spend in experimenting for that ever-dense pellet collection. Good hunting.