I wonder, is there a problem here to begin with?
Sometimes we interpret what we consider abnormal behavior on the part of others as a problem that needs to be fixed. This is not necessarily so. For example, a friend of mine has a wife who cries quite frequently (by male standards - i.e. maybe once or twice a month?). He told me that every time that happens he feels uncomfortable and tries to come up with ways to calm her down. This includes (a) distractions; (b) presenting the glass as half-full; (c) admonishion; (d) assumption of blame and escape, with inevitable period of 'bad mood' for a limited duration. After a while all this began to irritate his wife and she finally psychoanalyzed the situation, and asked whether he thinks her crying is a problem to be solved.
Why, indeed it is a problem when people cry, isn't it? We learn from childhood that cryling is kind of a 'last resort' of a response. Therefore, when this threshold is reached we assume that somethign has gone wrong to the point where it cannot be left unattended, and we rush to fix it.
Now the kicker: Turns out, not necessarily. To his wife, crying was an absolutely healthy and normal coping strategy with all kinds of crap. In other words, it was -- from her perspective -- her normal way of handling some kind of stress or sadness that happens now and then and is just a part of life. On the opposite, if she were to hold it all inside and let it build, it could have evolved into more serious psychological issues (like depression). Basically, she totally flipped the script on him. It turned out he was making a bigger deal out of it than she was.
In case you are interested, now when my friend's wife cries, his default is to let her go at it for a bit while minding his own business, then (after she is done) ask if there's something he can do to help, or if she wants to share, then (if she does) simply LISTEN FOR A LITTLE WHILE, without giving ANY advice or solving any problems, unless she specifically asks for it. Usually a 5 minute rant is all there is to it, and then they go on making weekend plans or whatever else. Non-crisis averted.
Could it be that an emotional reaction is Rainman's best strategy for releasing some psychological pressure, and if that pressure is not allowed to be let out in the best way he knows how, it could lead to deeper problems down the road?
The moral of the story is, we often make assumptions about others based on our own understanding of the world, and act on these assumptions without first testing them for validity. Could the moral of that story be applicable to this case? You be the judge, but I wanted to share this as something to ponder in relation to your Rainman. Perhaps freaking out emotionally is just how he handles mild constructive feedback, and it's not a judgmenta against either you or your team, and not a problem to be fixed. If this could be a remote possibility, I suggest a very brief informal 1-on-1 to ask him (very politely) that you noticed he has appeared a bit phased by some of the discussion in the meetings and seems to need time to recover.
Just share it as an observation and ask whether this is something you or the team need to be concerned about. Let him adjust your perception and suggest strategies for deescalating such situations, if indeed any deescalation is necessary or desired from his standpoint. Make sure to lace this conversation with a good-size dollop of praise.
I have a suspicion that letting him guide how such situations are handled may be the best approach, rather than assuming out of the gate that it's a problem to be solved and trying one tactic after another (possibly leading to some real issues down the road), when in reality this could be better off left alone. Letting go of a problem is sometimes the only right way to address it. In our action-oriented business culture we do not often consider inaction as an option, but sometimes it works better than anything else.
One last thought. If 80% of the 'emotional response' behavior is associated iwth Rainman's attendance of code review meetings, might it be possible to let him decide whether he prefers to attend those, or to communicate regarding the code in some other way? Perhaps he is much better at taking feedback on instant messenger, or by email, or in a one-on-one 'follow up' meeting with you where you share the outcomes of the code review that concern him, than in a group face-to-face format? Some people have handicaps in regards to specific communication modalities, which fall away and become non-issues in other modalities (e.g. that buddy of yours who always prefers calling instead of emailing, or vice versa). Might be worth a try - as long as it's cool with him and doesn't make him feel singled out or isolated, of course...again, let him guide this and you should be fine. Good luck!