Hevi-shot and Hevi-13 are two different loads. 2 years ago, I busted a tom at 46yds with Hevi-shot #6, he went down, but he flopped some.
Distance is the biggest consideration for shot size. Try going up to #4 shot and see what happens, but don't push it to stoopid distances. I'd try to limit my shots to 50 yds. If you want to test penetration at great distances (55+), do it on a target and not a turkey.