I have experienced problems in getting arrows to hit where I'm looking when changing from a bow that is cut past center to a bow that isn't cut all the way to centershot. However, for a given bow, I've been able to get different diameter arrows to hit in the same spot by tuning. I think you should keep working. A 5/16" wood shaft isn't really that large of a diameter, as wood shafts go. Probably by experimenting with different spines, arrow lengths, and point weights, you'll be able to come up with something that works.