ditto what Jason said. Another strategy with live plants is to use a light potting soil mixture just in the area of the plant itself. You can even keep it in a container you bury with whatever other substrate you prefer. That makes it a little easier to deal with plants that aren't doing well or lets you change the other substrate without bothering the plants too much. But the container does need to have drainage holes just like any other potted plant.

With you false bottom constrution you might look at some aquaponics/hydroponics methods and adapt those. As long as you are not growing garden vegetables for food <<grin>> you don't need the nutrient solutions. The frogs will supply enough ammonia.