It probably depends on how much weight you'll carry in it and your arrangement of belt loops.
I built one from 4-5 oz veg tanned, and though it works well, it just feels too stiff.
I built another from 2-3 oz, and that was fine stiffness-wise, but then I put a bunch of loose .600 balls in it, and it sagged pretty badly.
Version #2 made with 2-3 oz works fine with a heavier load, but I made the belt loop full length across the back to help distribute weight, rather than a smaller loop at either end. I don't like really heavy weight in a belt pouch, but if I was going to carry it consistently I might consider using 4-5 oz for the loop only, while using 2-3 for the body and flap. It might provide a way for you to go ahead and use the deer.