Czuch: Why would using the BKR at game start make more sense than the BKR at game end? As for a counter example, take a game with a 30 day move limit. At the start, my opponent has a rating of 2200. 4 weeks later, when he makes his first move, his rating has dropped to 1800. After his first move, the game is finished in a few hours. Wouldn't 1800 make more sense than using 2200 in this particular case?

The problem is that whatever BKR you use, there will always be an example that can be constructed that shows the choice was bad. Ratings will chance over time, and games here take a long time. There's no way around it. The only answer is to not take ratings too seriously.