Boys, boys, boys......tournaments aren't about finding the best team, it's about crowning a champion. My advice would be to bring it every night, if not, enjoy the couple of weeks off before travel season starts. Fairness? What's more fair than going head to head on the field?
Also keep in mind, in light of Title IV, pretty much whatever you do with Softball, you'll also have to do with Baseball, at least the IHSAA has followed that model. With their pitching situation in Baseball, I couldn't begin to imagine managing the pitching rotation in a double elimination tournament, three or four day tournament. You could end up with a #6 vs #7 in the finals, with a score of 19-17.
You should also be aware, that there are plans being looked at the restrict pitching in Softball similar to what Baseball does. I'm not saying it's going to happen tomorrow, I'm just telling you it's being talked about.