I agree with Pirandello. I think you're clutching at straws a bit OP.
You, as a couple, and he as an individual, do not have experience of dealing with negative feelings effectively. You have experience of him being moody and self-pitying (and quite possibly vindictive) for extended periods and you having to make a lot of effort to get him to see this and stop doing it. Every single time. Because, as Pirandello says, despite his apology, he hasn't apparently looked into why he does this, or accepted that it's important, to him, that he seek to avoid doing it again and again.
If you carry on like that, he's basically treating you as his emotional carer, the person who tells him what the rules are and sorts eveything out. His mum. Yuck. Who wants to have an adult, sexual relationship with someone who sees himself as a child and her as his mum?
Yes, babies and sleeplessness push everyone over the edge and yes, having relevant experience and tactics in place help e.g. people who've done shift work and long on-call hours aren't as thrown by the lack of sleep as others. But your DH needs to develop some tactics before you'll have any at your joint disposal.
I think there's an important distinction between someone immature who does want to have dcs and can be patient with small children and, someone whose moodiness, self-pity and manipulation are part of a deeper selfishness or desire to control.
The immature one can mature quite quickly when faced with a baby to look after and I've seen people like this, who are a bit unsure of themselves and their place in the world, really come into their own as hands-on fathers, fatherhood giving them a new purpose and identity.
The selfish, controlling one though (and remember this comes about through weakness and attempts to cover it, not any dastardly plan), will become more selfish and more controlling when faced with the total diversion of your attention that a baby brings.
What's he like with small children? Interested? Kind? It might be worth a bit of gentle acclimatisation with other peoples', as well as this giving you a helpful chance to observe.