ryoushi, I have a Benelli M2 dedicated turkey shotgun that I mounted an FF3 on. Spent more money than I would care to speak about trying to get the best patterns. The best I found was a Sumtoy .568 there was another that I will have to check for you it's in the shotgun right now at the camp. Probably tried about ten choke tubes and your on the right track if you can find one at .565 that should be good. If you want to try some of the ones I have send me a PM we can make an arrangement.
I settled on a load with 7TSS and as stated above it really slams a gobbler anything inside 35 is down without much movement at all Hevi shot magnum blend was good as well. I also have a lot of different shot shells I guess they could be mailed though not sure.
Good luck and shoot straight y'all
