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The mountains were very likely nowhere near as high as they are today. In fact, most of the mountains were most likely created after the Flood, as the water was receding.

You know the movement of tectonic plates is responsible for volcanoes and earthquakes? Earthquakes come about from plates moving very short distances, 30 feet max that we've seen (thank goodness). Any type of catastrophe causing sudden orogeny of thousands of feet would result in massive earthquakes and volcanic eruptions. The result would be a global extinction similar in magnitude to the disaster that wiped out almost all life at the end of the Permian--a global flood would look like nothing in comparison. Floating about in a boat wouldn't save you, and things wouldn't be getting better for, oh, about half a million years.