The second problem with transferring the house is that it probably violates the terms of the reverse mortgage. In any case, most reverse mortgages require that they be paid off within a year of the resident moving out of the house. I'm not sure why you haven't run into that yet.
All of this said, you really need to meet with a local elder law attorney to determine what steps you can take to protect your mother's house. Given what's at stake, paying the attorney to find out is a very small price to pay.