Crusader Kings seems absolutely and fabulously ideal for this.
The point of Crusader Kings is that it's a copy of Europa Universalis (which, in turn i similar to Civ) set in the middle ages.
The difference, however, is that instead of playing a country, you play a feudal dynasty. There are (historically correct) royal families (and lesser nobles) throughout Europe.
But get this. You play as the king, right? You marry off your daughters and sons, give your sons pieces of land. And once you die, you continue playing as your SON. Which is why this would work so ideally. Like. I start the game as the Swedish king. I have a son, give him land and croak. This son would then be played by someone else. Playing as each successive person is just like starting the game over, except in a different situation. In example, to get more vassals, i might have disbanded hereditary rule and instead set the most powerful vassal as the next king, which might not be my son. So i was concentrating on becoming more powerful, now the next player needs to concentrate on a coup.
The point being that we would have a much better swap points, rather than just arbitrary saves. I mean. It's almost as if the game was designed specifically for this. It's a relatively small game, give it a whirl, you'll see what i mean.
Problem being that nobody has it. But yeah, a good suggestion. We could do multiple succession games.