First of all welcome and congratulations on your new gun. I think you'll especially like the ShurShot stock. I put them on 2 of my 11-87's last year and like them.
I would certainly encourage you to try the choke that came with that gun. It's really very good. I've had several readers who've had good patterns with it and did not need an after market turkey choke.
I would encourage you to "deep clean" that barrel prior to shooting it. You can find an article entitled, "Cleaning a Shotgun Barrel" at http://www.allaboutshooting.com
that will offer some guidelines for that process.
From my experience, it's all a matter of matching the barrel, choke and shotshell to optimize the performance. I always have better patterns, not just higher numbers, with #6 shot than any of the smaller sizes.
Gun manufacturers pattern their products a little differently than most turkey hunters. They use the 30" circle, as has been pointed out, for reporting their results. Many of us use a 20" or more commonly a 10" circle for evaluation of our patterns.
From my vantage point, a good even pattern, without large holes is what is needed, not necessarily a certain percentage of shot or certain number of "hits".
I'd recommend you use some "big paper" at least 36"x36" with your new gun and choke and see what happens.
If I can be of help, just let me know and I'll do all that I can.