This sounds pretty cool, but could probably become a bit railroady, especially if it MUST be the same characters in each period. If you establish that the characters cannot die or become incurably insane, you might drastically cut down tension and drama.
QuoteWhos's the Great Elder found of arts ?
Which of the Great Old One you use doesn't matter that much. They are basically omnipotent anyway and their actions, plans and motivations are beyond human understanding in any case. However, Hastur is best known for having his own theatre play
The King in Yellow, which might work in the classic art context. Besides, Lake Hali and Carcosa could just as well be located within the Dreamlands.
QuoteAny reference to published material for each time period?
For the 1920s, you can use most of Lovecraft's tales themselves. Unfortunately, the story of him that actually is located in New York,
The Horror at Red Hook is one of his worst, utterly poisoned by the author's racism. There is also an official CoC suplement for the city in the 1920s, but I don't know how good that is.
For conspiracies across centuries involving Templars, Umberto Eco's
Foucault's Pendulum is a very solid read. The first (and maybe the second) chapter though are written to discourage readers to continue; the book gets much better (and accessible) later on.