I'm afraid you're wrong. Even with the dramatic (and unexplained) reorganization of the world's landscape you suggest occurred after the flood, there is still not enough water in the world to cover the land mass we observe. That's right, even if you smoothed off the mountains, it couldn't be done.
You yourself can investigate this. Get a deep lasagna tray, put in about 3/4ths water and 1/4th rocks and non-soluble dirt and such, piled into forms resembling earth's continents, ensuring that the solids are visible above the water level. Assuming fixed parameters for the coastal regions, you can now change the land masses to reflect any shape you desire. As long as each "continent" remains in the basic shape you started with, you will find that you will always have about the same volume of earth above sea level. This is because as you subtract earth from the "coastal" regions so they can be inundated, you must plop it back onto the continent somewhere else.
It's really obvious. And I mean REALLY obvious. Seriously. A little kid could figure that out. If I were you I would be extremely embarrassed to insist such a flood could occur.
The only thing God could have done to cover the whole earth with water simultaneously is flatten it completely (ie, change the shape of each continent) - tamp it down as flat and uniform as a tabletop so the water would lie on top.
But then, if he did that, why would he need the "deluge"?