Neither is really screwing it up too bad since the train cart part involves a cosmological part of VI's world that they never go into so they may have likely just left the train and boarded the next one.

They didn't really help Kefka become a god as much as they helped Gestahl attain the Warring Triad which Kefka then took from him. Basically there big screw ups were trusting the Empire after the Espers destroyed Vector. Even then, Edgar and Cyan were smart enough to be on guard in case of a betrayal but little good it did.