The short answer to your questions is you may be able to remove a name from a conventional mortgage when closing on a reverse mortgage. The precise answer depends on the circumstances, and the policies of the reverse mortgage servicer (the bank).
A sure-fire way to remove a name from a mortgage is to refinance the mortgage, during which one party (or more theoretically) is removed from the mortgage. This assumes that the remaining people on the loan qualify for the refinance. A refinance should not take longer than 90 days. (See Time to Complete a Refinance for details.) Here, think of refinancing as your Plan B.
Plan A is to start shopping for a reverse mortgage. Explain the mortgage situation at the outset of your negotiations. If the loan officer you speak to balks or tells you outright to refinance first, then carry on to the next company on your shopping list.
One place to shop for a reverse mortgage is the Bills.com reverse mortgage savings center, where you will be matched with pre-screened reverse mortgage providers that meet your criteria.
To learn more about reverse mortgages, see the Bills.com resource Reverse Mortgage Evaluation and Facts.
I hope this information helps you Find. Learn & Save.