Thank you everyone for your quick reply.
A booster club may be the answer, but I'll run it by my co.
Getting our robotics club classified as a team is possible, but unlikely.
The Parent Teacher's Association doesn't help much except hold our money. Sure I may be able to speak with the heads.
The only thing that the school provides is a facility to store and build the robot. We are still allowed to use those facilities. The main hurdle is that we cannot solicit various companies for donations. (Sponsorships they do consifer donations)
Negotiating with the admins seems the best way to go. But first I need to find out who made the rule.
Changing the name of our team may help. But I'm not too familiar with FIRST's policy about changing team's names and therefore losing the ability to pre register year after year after year. (I'm on Team 19)