from an issue of Scientific American. Thera blowing is just Thera blowing - now called Santorini - in 1600BC and it would have generated the giant tidal wave needed for the partying of the reed sea - but other earthquakes at other times would work as well to cause that particular - Moses -parting of the sea.
If the Exodus occurred during the end of the Hyksos era in Egypt as some scholars believe (16th century BC) then those Hyksos records of Moses would have been deliberately destroyed by victorious Egyptians as they drove the Hyksos out of Egypt. So no record of Moses other than the Hebrew one is all that we would expect.
Polyhistor, Flavius Josephus, Philo, and Manetho refer to him, as do others. Also, of course, there are the above-mentioned stories in the Mishna and Qur'an. A thousand years after Moses in the 3rd century BC, Manetho, a Hellenistic Egyptian chronicler and priest, alleged that Moses was not a Jew, but an Egyptian renegade priest. It has been suggested that he may have been an Egyptian nobleman or prince influenced by the religion of Aten (see Freud's theory). Moses is both an Egyptian name meaning "son" often used in pharaohs' names, and a Hebrew word (meaning "one who draws water" - Moshe). It was common for infants to be sometimes abandoned by the lower classes (in ancient times right through 19th century Great Brittan).
Exodus was around 1420 BC, since records exist of "Habiru" invasions of Canaan forty years later. Making the historical persona of Moses most likely the early 15th century BC Crown Prince of Egypt called Ramose, who also disappeared from Egyptian records around the time of Queen Hatshepsut's death; but it 1420 BC could be wrong and perhaps it was the 13th century BC, since tradition has it that it was Rameses II with whom Moses squabbled and the Seti I to Rameses II to Merneptah has the famed stele of Merneptah's 5th year (ca. 1208 BC), that claimed that "Israel is wasted, bare of seed", seen as propaganda covering up his own loss of an army in the sea.
Freud/Joseph Campbell liked the idea that Moses fled Egypt after Akhenaten's death (ca. 1358 BC) making Moses monotheism a derivative of the monotheistic religion of Akhenaten - and thereby taking the chosen people down a notch. It's likely the "Amarna Letters" written by nobles to Akhenaten were describing Hebrews when they referenced raiding bands of "Habiru" attacking the Egyptian territories in Mesopotamia.
Your idea that exaggeration plays a part in the Moses write up fits the idea that the plagues strongly resemble exaggerated versions of actual pestilences common in the ancient world, with the manna being the secretion of the hammada shrub, and the swallowing of Korah being an earthquake, and the Red Sea (reed sea) parting being cause by such an earthquake.
http://www.bbc.co.uk/religion/programmes/moses/ And then there is the idea that Moses and Akhenaten are the same person, except there is the problem that the religion of the Torah seems very different to Atenism in everything except the central feature of devotion to a single god.
The atheist claim that the old testament was actually made up for the first time by scribes hired by King Josiah (7th century BC), noting that no surviving written records from Egypt, Assyria, etc., refer to the stories of the Bible or its main characters before 650 BC, all fall apart when you note that the details of the Pentateuch are consistent with the earlier more traditional time period, such as the price of a slave (30 shekels as opposed to around 60 at the time of the Babylonian captivity), the practice of blood covenants and the discovery of what appear to be chariot wheels on the bottom of the Red Sea.
None of the above, including phrasing, is original with me and all can be found at various locations on the web.