I myself would cut out the bottom of the over flow and then screen it off from the tank. Then build my false bottom to be slightly higher than the bottom of the overflow so I could place a pump down in there for removing excess water or for running a water feature.

Having the pump down in the overflow would make access to the pump easy if you had problems later on such as it clogging up.

As Mike said, I would cover the overflow at the top so no frogs can get in there.