I know from experience you can use hardibacker for tile backing on walls, but whether or not you can use it on floors is unknown. It usually comes in 3×5 sheets, and is reasonably priced. What about using 1/4″ underlayment that is like an AC plywood that is smooth on one side? Check with your local hardware store and see what they suggest. Most stores will have a Contractor Sales area and the people are pretty concise about answering questions like that.
Work like you don’t need the money, Love like you’ve never been hurt, and Dance like no one is watching……