Thank you to all. I read through the CAR, but I wanted to make sure we were scoring correctly. It reads:
"If, during the course of play, another player completes a larger city—which means he or she places the final tile of this city—then he or she receives the King."
I definitely was trying to add to it rather than take it for what was written. Thank you for this site and for the rules. The clarifications and ability to print some things out and leave them with the box is key. This helps make sense of things without being called out for changing rules.
BTW, we are new to the game and do not have any expansions outside of the River that came with the original. We just decided to add the King and Baron element without the extra tiles. We have a couple of random pieces we use to signify these and then use the handy downloaded score sheets to keep track. It is a cheap and quick way to add a wrinkle/expansion to the game.