I think that if he is willing to go to his room and handle it on his own, then you are doing really well.
I don't recommend giving a 'punishment' because (in my house at least) that tends to lead to a spiral of more upset, more out of control, more punishment.
If you think that they are an outlet for frustration, you can make him a list of ways to (quietly) release frustration and ask him to do one of the things on the list. I would especially encourage practicing the things when he isn't having a melt down, so that when he is, they are already second nature.
I would also consider rewarding him becoming stronger and stronger at managing small frustrations well. Verbally praising even small examples of his power will wake him up to his own strength. I think getting him on an snack schedule, and getting him in charge of that is another way you can build up his self-control.
I think that a lot depends on how much the outbursts are bothering you. You are his role model of how a person deals with frustration. Do the outburst bother you because you are worried about 'what they mean about my son and my parenting?' or because they are loud and you don't like loud noises? I'm really really sure that the worrying you do about 'what shall become of us' is a bad use of your energy. Next time he does it,if it persists beyond the snack, try saying to yourself: 'Grinity promises me that this is just the normal side effects healing from underachievement, and when he has done 100 hours of this he will be done and healthy and a good boy and stronger than ever in his character.' If you can believe that- for even a few seconds - check how you feel about the outburst. That should help you see what percentage of your unhappiness is 'worry about the future' and what percentage is 'I just don't like loud noises.'
I'm not really promising that this is 'just a phase' but I do think that that is a reasonable approach for the next 3 months. It's really too early to start making major course corrections. Fiddle with food and exercise and mom-nurturing, and observe!
Love and More Love,
Grinity
