Are you sure it was a Green Mountain barrel in .62? Your title on the thread implies that is the caliber of your barrel though you don't mention the caliber in your text. I ask as Green Mountain doesn't offer such a product on their website. They offer a .45 smooth barrel with a 1" outside dimension, so is yours that product.., or is yours possibly a different make?
To answer your question, if it is a .54 caliber (28 gauge) or larger, a good load is the one that shoots well from your barrel. I'm not being a wise-guy, it's simply that with BP smooth bore guns, especially those that are not choked, or don't have a modern, screw-in choke capability, you really have to go out and try different loads to see what will work. Two barrels from the same maker, made one right after the other, may not use similar loads..., it's just part of the game.
Even when choked, you will find a "pet" load, for your barrel. I have a Pedersoli 20 gauge SxS, with choked barrels, and it loves 70 grains of 2Fg, and a ¾ ounce load of #7½ shot using paper wads. It doesn't like an equal load of #6 or #5 shot for some reason, and throws odd patterns. My 20 gauge trade gun (no choke) likes 70 grains of 3Fg, and an ounce of #7½, or #6, and when shooting shot likes two 1/8" fiber wads between the powder and the shot, and an "over shot card" on top.
The above mentioned load in the other response is fine..., some folks when going for turkey use #6 or larger shot up to #4, and use 80 grains (just about 3 drams) and from 1½ oz. to 1¾ oz. of shot.., and some as much as 2 oz. of shot! I'd say not to exceed 1½ oz. of shot...., and you will be going for head shots at under 30 yards.
Bottom line the "best" is the one you have tested on a target consisting of a turkey head drawn on paper at the range you intend to shoot.
LD