Even though the real estate market is saturated the time for you is now so go ahead and sell your house. The loss in value you will incur because of the down market will be made up by the loss in value of the property you purchase. Basically, you will be stepping sideways.
Talk to some lenders who handle the reverse mortgage to see if it is what you are expecting.
One caveat is in the event of your premature death your heirs will have 6 months to liquidate the property or the lender will take it and all of the equity in it.