You can't just say Hevi-shot. There is different shells and loads with this brand name. I shoot a winchester 1300 and if I shoot the 1 5/8 oz load in #6 I get crap compared to the 1 3/4 oz load. The 2 oz load is not too bad but still not as good as the 1 3/4oz.

Moral of the story is focus more on your second question. How to pattern. The rules of thumb I follow:

-You should pattern your gun out to 40 to know how it patterns out there. Even if you believ in getting them close. Know YOUR gun.
-You should be blasting a hole at 20 yds with todays chokes and loads
-You should worry about an even and consitent pattern across 10 inches and not focus on a picture of a turkey and the number of pellets in the head neck. A consistent pattern across 10 inches will a turkey. His head moves, your pretty target picture doesn't.
-You should polish your barrel and keep it clean when patterning.
-You should use a proper rest or set up. Your own mistakes should not lead you to believ your gun is off when patterning.
-you should NOT worry about what other guys shoot since every gun/choke/load combo can vary.

I also think since you're not target shooting or duck hunting spending a little extra $$ on a premium turkey load is no big deal. You might get 1 shot all season. Who cares if they are $2 a shell. It'd be different if you were shooting 20 shells a hunt.