Fincher should still fund that himself I think.
Gore Verbinski put together a team and they worked out the story and and boarded a whole version of Rango themselves before they got Paramount/Nickelodeon involved. Spent 16 months on it. Now granted he already got Johnny Depp involved before they took it to Paramount so that probably sweetened the deal. But I can't see why Fincher couldn't do something similar.
But Verbinski already had like a whole animation, story, and artist team assembles before he started making Rango. So he had his whole vision assembled without studio involvement and just did it all himself on the side after Pirates.