The time frame was MUCH shorter, and in fact that is a huge flaw in III.

The party celebrating Michael's getting into the Order of St. Sebastian or whatever took place in spring or summer of 1978.
The same night as that party, Vincent whacks Zasa's men and Michael tells him to work for him. within a matter of weeks Michael is bribing the church, getting their preliminary vote on the purchase of Immobiliare, and after the helicopter hit is in the hospital. There, Kay tells him that Anthony is already getting good notices (who gets good notices within weeks of announcing he is going to be in the opera?) AND that he will be starring in Caveliere Rusticana in Palermo on EASTER....which would be 8 or nine months away. By then
Michael is already set to hand the whle think over to Vincent who had been his apprentice for less than a year.