[EricH]

How about not having all of the students go to all of the events, or all days of all events? For example, let's say that you have 30 students and 3 events (2 regionals + Championship). Regional 1 is your "home" regional, Regional 2 is your "away" regional.

Regional 1, everybody goes to. It's close. Maybe half the team shows up late-ish on Thursday, the other half shows up late-ish on Friday, something like that. I've been known to not be at a regional until lunchtime Friday, or to take off early on Thursday and show up late Friday to deal with schoolwork.
Regional 2, between 15 and 20 students go to the event. Choose however you need to.
Championship, 15-20 students, but preference is given to those who did not go to Regional 2, or who are critical to the team's operation.

This is assuming, of course, that the school objects to every student going to every event. If they don't have any objection, then take as many as you want to to each event.