No real surprises here. Like was said, meeting someone one time - well even an insane person can fool some of the people all of the time. Not that your W is not sane, but I bet she was extra charming to the lawer.
What this does do is to confirm that the woman has the upper hand in the custody battle. If she wants the kids it is almost impossible for the man to win. Maybe next generation will be different. That is what happened to me - I am lucky for a 40/60 split with my kids; it would have been uphill in court to get anything better.
It is so easy to believe the busy focused surgeon is not the best full time custodian. It is so easy to believe the stay-at-home mom of a busy doctor struggling to raise the kids almost by herself. It is so easy to disbelieve that a doctor of all people could not have the money for mortgage payments and such (he must be hiding money or paying for a mistress).
It all sucks. All I can suggest is that you cut a deal. Going into foreclosure is not good. A credit rating is as important as the license to perform doctoring. But if she will not agree to sell what can you do?? Go for joint custody, 50/50 is better than the alternative.
Good luck FIB. It is time to get it done and behind you.