I would do what others have suggested of timing the scream-cry and deducting time for the next day. I do think I would give him a short "grace period," though, and I might start it out on the long side and then reduce it. So, say, for the month that you introduce the system, he is allowed to cry for 15 minutes after being cut off, but then you start the stopwatch to figure out how much time to deduct the next day. Next month, his grace period goes to 10 minutes, then 5, then 3, then 1.
The down side of this, of course, is that you have to listen to the scream-cry for at least the grace period, and probably longer until he accepts that you mean it. And you'll have to decide what "counts" for running the stopwatch.
Try to talk to him about it on a day when he normally doesn't get Minecraft time, at at time of day when he is in a good mood. Do what you need to do to make that happen, even if it's hiring a neighborhood teenager to watch the baby for a couple of hours while you spend time with your older son. Ask him for his ideas before you introduce yours, and don't accept, "I promise not to scream" or "I'll try harder" as solutions.
If you haven't read it, The Explosive Child is all about kids like this, and its system does work if you keep at it (give it at least a month before you give up).
