We are a community based team - we have no school support and we have kids from 6 or 7 different high schools along with a large group of homeschoolers.
I think there are lots of advantages to being a team without a school. Of course filling something into the "school name" in the FIRST paperwork is always interesting
The group of mentors/leaders that started our team created a non-profit, a 501 (c) 3: The River City Robots and under that is The Channel Cats, team 1094 and we've had 21 Lego teams in the last 5 years.
Hang in there - anything is possible!
DeAnna