I understand a link from the game screen to the specific play in the log might be hard work, but I suggest a direct link from the game screen to the log so that we can find a play without having to go through the league home page and see the final score

That's actually on the 0.2 roadmap, I agree that it would be very helpful. I plan to use your idea from the beta testing where going to the log will only show you the log up to the play you left the game center from, and have a link to get you back to where you left off.