when you refi the house, that would mean you are going to borrow $96,800 on a home that is assessed at $99,000? For some reason, I'm not seeing this as a reality.

If you can do that, you are allowing her to cash out her equity in exchange for relinquishing title. Unless a true appraisal of the home provided a different value, I cannot see what would be wrong with what you are doing. After all, you will be paying off all the debt that is in her name when you refi the house so she would not be including that debt in her BK.

A trustee will likely review the transaction to be sure it wasn't fraudulent but from what you have said, no creditors would lose anything here and your ex will be paid a fair amount for her interest.