The diameter of a wood shaft needed to obtain a specific spine has to do with where it came from in the tree. Shafts made from a large tree that are milled closer to the heartwood will be denser. In that situation a particular spined shaft can be much smaller in diameter than a shaft from the same tree that is milled from wood nearer the outer layers (sapwood). In general, a good wood shaft can come from only a tree that has straight a straight grain. Changing the diameter of the shaft does not change its quality unless there are surface irregularities, and making the shaft smaller will only decrease the spine.
By the way, most of my life i have always preferred a smaller diameter shaft. For hunting they are better for penetration. Since they are denser, they are generally tougher. As far as i can see the only benefit to a larger diameter is that if you are competing the larger diameter may give you a higher score because it will more likely "be a line cutter" on those shots close to a scoring ring on a target.