Arikay-
The tallest mountain of the time was Mount Ararat, so Everest wasn't 6 miles high back then. Now what makes you think, with all the plate tectonics going on, that Everest couldn't rise to its present height from the Asian and European continental plates colliding, over 4000 years?
A volcano in Mexico rose to like 1000 feet in a week. Yet no catastrophic destruction of Mexico resulted from such an abrupt rising of the volcano, so what makes you think the other mountains would be any different? God created boundaries to hold the flood waters in Genesis, and the "fountains of the deep" gushed opened, so im sure there was pretty catastrophic geological events going on during the flood, but under so much water, what makes you think heavy continental collision would boil off all the water? Ever seen it happen?