Kostya, I don't see a better system than "lose and you're out." If you have any ideas, let me know. People will have a choice: either drink or play – and I'll make it tough. You can always give up and go have fun. Maybe I'll slightly reduce the timer.
Actually, 4 rounds on normal maps barely fit into 4 days, let alone 2. And only blitz formats can maintain a pace of more than 1 game per day.