The election was not at the end of GH's turn really.
As I posted back then when GH's first incarnation whacked Gregory and the others (and was decried for revealing an "exploit" which it is not), whenever you load a savegame that does not have an elected pope, the game will pop up the election screen allowing you to go through the entire college in 1 turn if you wanted to (whack, save, load, elect, whack...)