You can't rush shoot shafts. Like bow wood they need to season, but they don't take as long.
Cut them as long as possible, leave the bark on and don't seal the ends. I bind them up with string or zap straps. Every day or 2 take them out, hand straiten and bind them back up. This will save a lot of time for heat corrections later. After 2-3 month (longer if possible)some of the ends will check but that's why you cut them long. Remove the bark and bind them back up. This is when I start weighing them.
When they stop losing weight, make your shafts. Its easier to heat straiten when they're long, then cut them later.
Different species will require different thickness, so you'll just have to experiment. I like cutting them a little bigger then planing them down till I reach my spine.
You should really be looking for mock orange aka syringa, it's awesome arrow wood, beautiful wood, and if you can find a big enough piece it'll make a bow.