First of all, welcome to the T&TH forum. We're glad you're here and look forward to hearing more from you.
Patterning a shotgun, trying different chokes and loads at various ranges certainly does represent an investment of time and money and you've done a good job of documenting your results.
Strictly on the basis of what I see on your chart, the Hevi-13 shells with the JH choke would be the one that I'd choose, from what you shot.
Just as an observation, I always recommend that a hunter pattern his load of choice under several different weather conditions that he's likely to encounter during the season or seasons that he's likely to hunt. A cold and damp day may influence both the pattern density as well as penetration, for example.
I also recommend that you start with a squeaky clean barrel, "deep cleaned" http://www.allaboutshooting.com/article_info.php?articles_id=282
and shoot several of the same shells, though the same choke, without cleaning between shots, to see if that combo prefers a clean or slightly fouled condition. When you change shells or choke, I recommend that you deep clean again.
The only comment or recommendation that I'd make with your 870 is that you might want to try a little tighter choke with the H-13 shells. I see my best patterns with 870s with the 3" Hevi-13 "Bronze" shells with 2 oz. of #6 shot and the SSX turkey choke which has an e.d. of .643.
Again, great to have you here and all my best this spring in the turkey woods.