Continuing this post.
Q: How many divorced men does it take to change a lightbulb?
A: Who cares? They never get the house anyway.
There are additional reasons to permit this man to take a second wife:
1] The Rema paskens that if one doesn't have children for 10 years with the first wife, he may take another and there is no cherem d'rabbeinu Gershom. In our case he will never have children with this women whom he can't be with because she is a ספק אשת איש. So of course we permit him to take another wife.
2] In Yoreh Deah [127/3] it says that the rule עד אחד נאמן באיסורין means that one witness has the power to PERMIT but not to forbid. In our case we must rely on the testimony of the first husband in order to assume that she was divorced and it is thus forbidden for the second man to take another wife. One witness can't forbid - he may only permit. [Also - the circumstances of this case were quite shady - see the Teshuva in Eretz Tzvi 124 for details - so it is difficult to believe him].
3] Even if we wanted to believe this man that he divroced her it would be difficult because he is claming that he divorced her sinfully - there is a cherem d'rabbeinu Gershom not to divorce one's wife against her will. We have an iron clad rule אין אדם משים עצמו רשע.
Bottom line: Let this man get the signatures of one hundred Rabbonim as is the law of a man permitted to take a second wife and he may remarry.