The debate about when to bevel is interesting. However, I don't think it is helpful. When all is said and done, some people need bevel, some do not, and there is no magical formula for determining who does.
The first question should be whether the lack of bevel is causing him to hang, and second, whether beveling the whole will solve the problem.
I do not claim to be an expert on bevel theory. However, I am confident that if the lack of beviling or your drill specs were causing the problem, you would hang from the first pitch. Again, if seeing you release the ball while not hanging, and seeing you release it during the third game when you are hanging, would help to determine what is causing your problem. Without seeing, my best guess, based on what I have seen, is that the problem is either you are grabbing the ball, or the ball is hanking on your thumb, likely do to your thumb shrinking or swelling by the third game, or that your mechanics are changing by the third game with you coming around the ball too fast, causing it to hang on your thumb before your thumb clears.
Try concentrating on staying up the back of the ball during the third game and see if that fixes your problem. Also, if your thumb whole seems lose, add tape until it is nice and snug like it should be.