...All three games and still have it make sense/ not go into conflict with lore, plot, npcs, etc?

The first issue that comes to mind is the epilogue as told in Oblivion.

"They say the Nerevarine has gone on an expedition to Akavir".

They could say a lot of things but nobody we meet knows for sure what happened to the Nerevarine. There is only rumor.

I think that if you're playing an elf or other long lived race or character (necromancer), this could be possible. If I remember correctly, the time period between Morrowind and the events of Skyrim are only about 220 years (20 b/w MW and OB and 200 b/w OB and SK).

Don't play through the main quests. At least Skyrim's, anyways. I can see Oblivion's MQ working, though.

Also, the Akavir rumor is nothing more than a rumor. Note the "they say."

The Nerevarine's Immortal, 'member? Unless you meant social problems like the ones Janus Hassildor faces for being long-lived.

well, the Nerevarine is immune to aging..

however, it would draw up to many Inconsistencies for me.. Why do the various Daedric Princes always talk to you as if its your first meeting? why doesn't Neloth recognize you when he is talking about the Nerevarine (and why you didn't say "ohh but I do know of him, he is me!"), what happened to all your Artifacts such as Trueflame or the Moon and Star, if you were Dragonborn than why were you unable to wear the amulet of kings? why have you lost all access to the spells and powers you had gained?

there are many more if you would like more examples on inconsistencies..

Oh my, how could I forget!

Of course, knowing that they are immune to aging, maybe corprus was just like an anti-wrinkle cream for life? Since I believe we're told that the Nerevarine is immune to aging, not necessarily immortal.