I really like your point here because it echoes some points I brought up myself....
This reasoning creates a catch-22. For a global flood to have any merit, the mountains had to be lower, as there is not enough water on earth to cover Mount Everest, whereas if mountains were lower than today, less water would be needed. However, this means after the flood there were monumental land transformations, with mountains being pushed up out of the floodwaters. Mountains usually grow at a rate of only millimetres per year, and even then the result of such movement can be earthquakes. For mountains to have grown thousands of metres over a rapid period, the resultant earthquake activity would have made the earth uninhabitable, in a state of constant, violent movement by earthquake and volcanic activity. What the waters had not destroyed, this continental reshaping would have, removing the majority of archaeological trace of life from any time prior to 4,400 years ago. Yet neither the Bible nor recorded history discusses such upheavals in the period after the flood. Earthquakes are a sign of the last days, yet modern quakes are almost inconsequential in comparison to what would be required for Everest to form after a flood just 4,400 years ago.
The Himalayas arose via the northward collision of the Indo-Australian Plate into the Eurasian Plate, folding the ocean floor of the Tethys Ocean and lifting it along the convergent plate boundary (as opposed to other plate boundaries where subduction of the seafloor occurs). The majority of the uplifted rock, meanwhile, was eroded away via yearly monsoons to produce the many foothills and landforms south of the Himalayas. To have this all occur in just 4,000 years involves an impossible speed of plate movement. The distance the plate would have to move is in the thousands of miles (over 3,000 miles), which means that the Indo-Australian Plate must have a velocity measured in miles per year as opposed to the actual speed of 67 milimeters per year it presently has (as measured by GPS). Think about that. To put things into perspective, the 2004 Indian Ocean earthquake was the second most powerful quake ever recorded, 9.3. It produced one of the most devastating tsunamis in recorded history. The plate shifted about 20 meters in this event. That's it. How long does it take a person to walk 20 meters? "Hyper plate tectonics" would require plates moving thousands of miles very quickly. This would have, say, the Indian subcontinent move countless times faster than the seafloor could be laid down at the central and southeast Indian mid-ocean ridges. Such a speed would also posit an impossibly immense amount of friction at the collision boundaries, fracturing the lithosphere and triggering a flood basalt event that would have surely dwarfed the Siberian Traps. Nothing like that ever occurred, nor even daily 9.0+ earthquakes throughout recorded history, and there is no mechanism for such a ridiculously fast speed (certainly not normal mantle convection).
The process was geologically slow, as it took yearly monsoonal erosion to produce all the foothills (which would constitute large mountains by any other standard) south of the Himalayan peaks. Don't just think of the amount of uplift required to push land up to the height of Mount Everest, for Everest itself was being eroded down as fast as it was being lifted up. According to surveys of the Himalayan plateau, a total of 5-9 km of vertical rock was eroded from the Tibetan Himalayas and about 12-25 km from the Higher Himalayas. Compare these figures with the height of Mount Everest, which is only 8.8 km in height. So the height equivalent of one or two Mount Everests have been eroded away throughout the whole plateau as the Himalayas were pushed up. And considering that under normal monsoonal conditions 2.9 mm is eroded away per year, it would take millions of years of weathering to accomplish this feat.
The Society also likes to mention seashells in the Himalayas as evidence that the Flood covered the entire earth. This ignores the fact, as mentioned earlier, that the land uplifted into the Himalayas was originally oceanic crust of the Tethys Sea. Go to the supermarket and buy some pink Himalayan salt mined from halite evaporite deposits laid during the drying up of the enclosed sea.