I like the idea you linked to, too. In fact, the first version of that "have more stones on the board" is exactly how I explain the rules of the game to beginners. They pretty quickly realise the tediousness of filling in what's effectively already owned intersections, at which point they're ready to hear that "normally, experienced players don't actually go through the trouble of filling it in, they just count it as theirs. If there is any dispute about whose it is, play resumes until it becomes clear again."