The elephant in the room of this “purely” Halachic discussion, is that the man is looking for a heter for polygamy because he is refusing a Get to his wife, but he’s unwilling to suffer the consequences in his own marital life.
He is handing her a living death sentence and guilty of violating tens of aveiros chamuros along the way. The hypocricy and self-delusion of caring about CDG while ignoring the foundations of what a Jew is all about, is astounding.
Let’s not minimize this that it’s about being a “mench.” This is about the basics of Torah.