David Ellison's Skydance Productions will finance two-thirds of the budget, with distributor Paramount picking up the rest of the tab
Director Alan Taylor wants "Games of Thrones" actress Emilia Clarke to play Sarah Connor, but Paramount favors "Short Term 12" star Brie Larson
Goldberg had been president of production, but the promotion comes as Skydance expands into TV
Skydance and Paramount productions include Brad Pitt's "World War Z," "Star Trek" and "True Grit"
The studio had planned to release the 3D movie on June 29, 2012
David Ellison's company will finance at least four movies a year