That is quite a normal weight for 5/16 Birch and I would even have guessed a tad more. Most woods can vary by as much as 100 grains and even more. I have had cedar full length 11/32 that weighed 400 gns and those that were 550 gns. I usually buy large quantities and sort them into groups.
What is the variance in weight among the 100 birch shafts that you bought and what about the spine?
I have shot Birch a lot-makes excellent arrows. Sounds to me like you have the process under control!