It appears that the mortgage company does not understand the business form of a sole proprietorship.
The sole proprietorship is not a legal entity. It simply refers to a person who owns the business and is personally responsible for its debts. Some states may have registration requirements.
I would discuss with them that this is not a legal entity whereby you can formally dissolve the business with the state as in many if not most states, there is no requirement to even notify the state of the business form; unless of course you have employees, collect sales tax, etc.
I would then ask them if your providing them a letter stating that you have "closed" your sole proprietorship and sign the letter under penalties of perjury would be sufficient to move forward. If not, you may need to invest in an hour or two with a local real estate attorney to help you resolve this matter.
*A reminder that posts in a forum such as this do not constitute tax advice.
Also keep in mind the date of replies, as tax law changes.