This is all personal opinion with no data to back it up.
This is something I struggle with as well. My STBX and I do not "co-parent". We have had not had any kind of discussion about common ground, how we want the kids to be raised, etc. My sitch is a little different in that I have girls 80-85% of the time.
Like you, I wanted co-parent counseling but was worried about it derailing what has been a relatively smooth divorce process (in terms of custody and property settlement).
Here's where my thinking has gotten me. Much like marital counseling, I don't think any kind of parental counseling is going to go anywhere right now. STBX is just not in a frame of mind to really hear any of this. If he showed up, I think it would just be him trying to prove how "reasonable" he is, and he would then continue doing whatever the heck he wants. From what you have written, I can't see your WAW being receptive to any suggestion that, say, OM not be allowed overnights while boys are there.
I really can't see anything constructive coming out of these conversations...now.
I can't imagine my STBX being this way forever. Maybe when the divorce is completed, and he feels "free" of me, he will calm down, stop seeing me as the enemy and be more open to some hard conversations and cooperation. I think it will help when his current relationship either ends or solidifies into something permanent.
In complete fairness, my STBX is more civil than yours, so its a lot easier to envision this happening.
Have you looked into whether you might have any recourse after the dissolution is complete to prompt her to go to counseling or put together a parenting plan?
