Kids can have a phase of developmental stuttering that can seem just as severe as more long term stuttering and there is not a wonderful way to predict if it will continue or not.
There is some thought that if you point it out in any way you can accidentally increase the worry of it and make them more aware so it can become worse or they can develop secondary characteristics such as eye blinks head shakes etc...to try to stop the stuttering.
The family should seek a Speech Language Pathologist (SLP) consultation to make sure that these things have not already happened and because there are some nice child friendly techniques that can be used if there is a thought that this is true stuttering.
Most of what you are doing is perfect. TeDo is right on...get down to their level, keep eyecontact and show no impatience. Model slow speech in what you say but do not tell them to slow down. There are other ways to slow them down but the key is to make sure you dont pair it to ONLY those times when he is having dysfluencies. Like if he calms by sitting on your lap, put him there every time you have a conversation. or if he likes his hands held to see you are paying attention do it every time you talk to him. You can take a deep breath just for yourself, but it shows how to take a deep breath and use a soft speech style that is not excited and loud.
It is neurological and as with all neurological things it can be made worse by excitement, stress, being in a hurry, transitions, competition for speaking time, etc. It is not behavioral or to get attention which it seems you know.
the main thing is, since people who do really develop stuttering suffer with self esteem issues very often , to make it a non issue as much as possible. Never allow other kids to mimik or tease.... at that age they would not likely be doing it to be mean but just because it is different and they copy things so distract the offenders by just getting in the mix and talking about something else or bringing them toa cool toy.
Hope that helps.
There are many different theories about how to deal with this but I stay pretty conservative because I would not want to be the one to accidently increase the issue. then allow the parents to decide with a therapist who has evaluated him if there are any other techniques to be used and when. JMHO, oh and that's right, it is what I did before I became stuck at home mom. OH I mean a stay at home mom, lol