You're going to get a lot of pusbcak by saying the Oscars was mostly right when it gave 8 Oscars on the year everybody thought Godfather was going to triumph. I'm not sure Coppola got over when it happened.
Incidentally Fosse made five films and was nominated for Best Director for three of them: Cabaret, Lenny and All That Jazz. Each year he up against Coppola for Best Director (Godfather, Godfather II, Apocalypse Now). Fosse took the first round, Coppola the second, and the third time out it was a draw as the big winner was Robert Benton's Kramer Vs. Kramer. Fosse is clearly the gold standard for the most successful Broadway director to crossover to film - his other two movies Sweet Charity and Star 80 are also highly praised in many circles. I would welcome your thoughts on those four other films if you've seen any or all of them (they're all on DVD; I don't know their streaming availability)