IMHO, it is difficult for the LBH to distinguish being friends and just showing a polite, friendly manner. Especially when there has been no break or space in the relationship, he gets sucked into her personal life again. Plus, as I have said before, the WAW'S idea of the friendship and the LBH'S idea is usually quite opposite. He (the LBH) is thinking the friendship will eventually develop into more between them. And honestly I believe it can and does happen........once the couple can get past the hurt and anger with each other. But to jump immediately from being cheated on to being great friends? I believe they have two agendas in mind. It is very doubtful the WW, who is still in an active A, is thinking about getting back into an intimate relationship with her H. Her agenda is much different.
Don't get me wrong, I do believe in doing what works. HP couldn't control his anger and she wouldn't control her endless contact. I wished he could have had a long vacation from her, but.....oh well. So again, I suggest you proceed with caution, HP. Take this very slowly and do not get drawn back into her manipulation over confusion of the term "friendly". If you start questioning yourself about what kind of friend you are, etc., then you've slid too far the other direction.
You told her you were moving on, so act as though you are already D and you are being nice and friendly toward the mother of your son. Stay balanced and don't lean too far in either direction. Also be watchful that you do not start pursuing her, under the guise of being friendly. At least for a while, have the mindset that you are strictly co-parenting. Pretend you are co-parenting with your neighbor down the street. Don't get too personal, for now. The mistake I see many H's make is getting into the BFF trap b/c they try to get too close to her too quick.
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!