Ok. So you want to use this point system for use in scoring during tournaments. Not for anything else, correct? That might work. Perhaps a 'Offer 2-point loss' button (like an 'Offer Draw' button in chess) could be added to this site. That would help too.
But don't certain lines tend to lead to wins without the chance of P2 getting his 1 point, while others do not? For example, the wedge often ends 5-4 on pairs (at least when I play ;-) ), while the Boston opening usually does not, so even an expert P2 might not be able to get 1 point depending on which opening his opponent chooses. Is that fair? I'm not sure.