Unless someone Comes up with a better solution, this is my ruling
Ok, here's my perspective.
1. One won set can't be better than another won set. A win is a win.
2. Each of us beat somebody and lost to another.
3. None of us can really claim that we "won", unless we disregard rule 1.
4. Therefore, I would declare this a 3-way tie.
5. I don't see a way to determine a real winner in the future.
6. Either all of us deserve to get a spot in the tournament or none of us.
7. Obviously, at least one of us deserve to be in the tournament.
8. Therefore, all of us deserve to be placed into the tournament.