Cycles are for repeating, not ending.
The Native Amerincans say the Mayan cycles would bring a big change, but the cycle would start over.
As for the Electoral College. Remember that when it was made, there were still many states that did not choose the President by popular vote at all. The Electorate were picked by the State Government (usually the state legislature) and they picked the President. The popular vote might have influenced them, but I doubt it. (In the
Election of 1832 you can see South Carolina give 11 electoral votes to someone that wasn't even running for President)