This sounds totally like stress. Stuttering increase with stress and anxiety. Anything you can do to help lessen that may help. Look up age appropriate meditation practices and breathing exercises maybe disguised as Games and make them part of his routine. Do them with him and you all can enjoy some relief during this anxious and stressful time. I’m not a parent, but it seems to Me that kids, when excited talk a mile A minute right? and stuttering probably occurs during that? You probably want to avoid just telling them To “slow down!” or “Breathe!”. I don’t have good Memories of My Grandmother saying those to me. This may be the time to invoke those meditation or breathing games and make sure to do them With him. As much as we hate to admit it, sometimes having a better flow of air can help. Is he starting to read? If so, reading to you in a nice calm environment which I’m sure You already do may have some positive effects.