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I personally have never heard or read where a YEC (which I am) claims the flood was caused by melting icebergs. Regarding the flood, we typically believe just what Genesis 7:11-12 states. "In the six hundredth year of Noah's life, in the second month, on the seventeenth day of the month, on that day all the fountains of the great deep burst forth, and the windows of the heavens were opened. And rain fell upon the earth forty days and forty nights."
God caused the water deep within the earth to burst forth, which seems to be evidenced by the mid-oceanic ridges. We also now know there is water within the mantle. Also, see hydroplate theory at http://www.creationscience.com/onlinebook/HydroplateOverview2.html
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YEC proponents attempt to show that supernatural causes have natural effects that persist across a long time scale, hence can be discovered by studying nature. They believe that these supernatural causes can not be explained by a purely naturalistic science. Because of this, you can use these imprints in the earth to discriminate between the Genesis account and the old-age, evolutionary worldview, showing one to be more consistent with the geologic record.
The ice ages come into play in this scenario:
The fountains of the deep broke.
Large quantities of superheated water entered the oceans, raising the sea temperature and sea level.
The accelerated evaporation from the heating filled the skies with much of the water needed for the flood.
Some of the flood was tsunamis from the volcanic activity, some was rain.
The massive vulcanism during the flood raised the mountains and caused the sea floor to drop. This became a receptacle for much of the water of the flood.
The volcanoes spewed so much ash into the air that it blocked the sun for decades, causing the first and greatest ice age. This deposited enough ice to take more of the water out of the system, lowering the sea level.
The seas began to cool.
The shock of the volcanism and flood created a ringing within the earth's magnetic field, causing the frequent pole reversals.
While the water covered the earth, the single original continent split apart. Had people lived on land during this, they would have died. The flood protected Noah and the others from the reshaping of the earth during the flood. The presence of much water reduced the friction, enabling the continents to move hundreds of miles quickly, but slowing down after the water was squeezed out, to the rate we now see today.
Most of the fossil layers we see were created by the flood, though additional layers have formed since then. The high speed current flows caused hydrological sorting by size, leaving smaller organisms at the bottom and larger ones at the top, which combined with climactic zone and elevation sorting, create the illusion of a pattern from less evolved to more evolved. Smaller creatures usually are simpler, and sea creatures would appear first in the record, with land creatures on top.
etc.
So what the model is trying to do is show that natural processes accelerated due to unusual miraculous events, but left traces that can be studied and compared to other models. They were not miracles that left no trace.
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I'm not going to try to address the specific hypothesis. Instead, I'm going to focus on the question you ask in the title, and:
why [don't] young-earth creationists [...] leave any room for miracles in their explanations of things that are commonly regarded as miracles
Why? Because they are scientists. Science is about studying the inherent order of God's creation. Science originated in Christianity, because God prefers to work by creating a well-ordered system that (with some exceptions which are called "miracles") functions according to rules. This, when it was first conceived, was in contrast to pagan religions in which the gods manipulated the physical world according to whim.
A genuine scientist will, therefore, do two things:
These, and additionally treating the Bible as a generally reliable historical account, are the principles under which YEC scientists work. They are generally very forthcoming about these principles. This is in stark contrast to Naturalists who ignore the second principle and thus run smack into the Holmesian fallacy.
So, it isn't that YEC's don't leave room for miracles, but rather they recognize that God usually acts within the laws of nature and therefore seek to increase in understanding by attempting to learn about those laws and how an act may have been accomplished according to them. Doing so is the very definition of Science. Failing to do so is to willfully remain in ignorance. Had we done that, we would still believe that disease is cause by "bad humors", that mice are spontaneously generated from grain, and all sorts of nonsense.