He sounds like he has some wonderful qualities and potentially adopting the moo's brat is one of them.
And he is concerned he is the asshole, too. Sounds to me like the "victim" moo has found a new male abuser to make her feel like a victim but wants to keep the wallet intact.
He sounds naive and moo saw him coming and played on his emotions/manipulated him with her brat. She has her "victimhood" story down. And she is trying to manipulate him with more "poor me" stories while divorcing him. It makes me wonder if she gaslighted him too, as it seems like he is doubting his own judgement. Perhaps she has passively aggressively suggested he is an asshole for not obeying her every command. He may also have grown up the product of a single parent, which may cause additional sympathy towards her and guilt for the brat.
I bet the moo is looking for a way, any way, to stick him with a payment. Probably found out alimony doesn't pay out in such a short marriage because they likely haven't been married even five years because her kid is only five and from her "abusive" ex.
If it isn't about money
then he could offer to visit with the brat regularly as a friend. Say a park or similar once a month for a couple of hours. It may assuage his guilt (which I would argue is unfounded) and it would likely expose the moo's true intentions that all the rest of us are well aware of. If it were really about him being in the brat's life this would suffice.