Praise be! Thank you God!
Really glad to see you considering updating, and hoping that you do update. 
As for your point about Richard Nixon, I agree that it's unlikely for the exact same person to exist with such a POD. However, it is, IMO, better to use real people than just start making people up. For one, there are no photos of these fictional people, two, it takes away from the background of knowledge that readers already have of the person, and three, it takes away from the "coolness" aspect of having _________ be Prime Minister.
Using real people also gives the reader something to compare back to...like if Bill Clinton popped up as a conservative...etc
