I'd like to make a suggestion for a minor adjustment, which is really just a suggestion, ya'll can hate it if you like.
For the points system Swizz made, I'd suggest also making a 2 point difference between 3rd and 4th as well to give a little more significance to a podium finish than not. So something like:
It really depends though, because using Swizz's math a team with a 1st and 4th place will win over a team with a 2nd and 3rd place team, whereas what I suggest would see them tied. I do think it will become more important though if 3rd place is the highest finish of any player on 2 given teams, then the fact that one of the team members has gotten on the podium will be just that little bit more beneficial, which I think is the bee's knees.