Ah, but they weren't conquered, so it's not like they've been forced to move, and as they were still allowed their own practices and government because of the Armistice it's not like they're looking for work or to move into a 'civilised' land, either. The reasons you gave are all okay (except maybe the Great House conflicts, which seem to have been conducted via the Morag Tong rather than open warfare before the start of the Oblivion crisis, and most Dunmer in Cyrodiil, in Cheydinhal, especially, seem to be recent immigrants), but they wouldn't make the Dunmer the third largest minority in Cyrodiil.
The Chimeri Exodus was a religious divide. It's not in their nature. What is in their nature is racism, xenophobia, and Elven arrogance, not to mention contempt for Imperial attitudes (evidenced by Dervera Romalen in the game Oblivion) even amongst the more tolerant Dunmer. The large number of them in Cyrodiil has to have been influenced by something other than the need for change, and something very unusual (which would rule out ongoing House conflicts).
I suppose the Blight may have been involved, but then only a minority of the Dunmer in Cyrodiil actually seem to be from Morrowind (Ulen Athram, a trader from Kragenmoor, and Dervera Romalen herself don't appear to be). In fact, the only Dunmer who I've heard mention that she's from Vvardenfell is Llensi Llaram. So the Blight, whilst it is a factor, may not be a major influence of the emmigration from Morrowind.
They were not conquered by the original military force - they were conquered by betrayal from within by both Vivec and his Hlaalu friends.
However the Empire prosecuted a war of conquest on Dunmeri soil - while all was peaceful in Cyrodiil - so mnay in the path of those armies may have seen their lands, possessions and livestock appropriated by the invading Imperials. Others may have lost their jobs and been unable to find new - collaborated with the Imperial Armies and decided to flee when found out or accused etc. All these people would have found themselves forgetting the details and many would not have wanted to tell their children about what they may have seen as their own failures or those of their people and God/s.
About the Exodus - surely there was a massive religious divide and also, maybe just as important, persecution by the Altmer? - but I wonder how many disagreed about the destination or simply did not want to follow those who went to Morrowind or decided to go by another track and then liked the places they found, intermarried, whatever.
About their nature - some of that would be innate and some created by circumstance. The Ashlanders are Nomads - and they believe they are closer to the old ways than the Great House Dunmer. Note that it is claimed that when the Chimer and other modern mer arrived in Tamriel (before they became Chimer then Dunmer, Bosmer, Altmer etc) they met mer with their original ancient, civilisation intact and those mer considered them all to be primitive nomads ...
Again re House conflicts - I was not only thinking of small hands-on combats or assassinations - I was also thinking of trade routes and access to resources cut off, fraud, theft etc ... the vast array of 'civil' and criminal weapons that make up the Hlaalu Modus Operandi. You might consider how the Hlaalu rose from being a Minor House to being a Great House and came to have control of so much Redoran Land even before Vivec betrayed the Dunmer.
There are a lot of variations on the above possible when you look at personal motivation. But the last but not least is that th eDunmer in Cyrodiil have been infected with the Imperials' over-inflated view of themselves and either are ashamed to be thought of as Dunmer or are worried that they might become subject to racist persecution if they push their Dumer background - note that 'Dun' Mer in Cyrodiil are now 'Blue' Mer.
A lot of people move because they want to leave things behind them.