Don't be fooled by the list of "official teams". I get correspondence from teams every few days asking questions and indicating that they are working the mission at home. I'll send out another notice soon as a reminder that the registration deadline is approaching.
Regarding sponsors, they usually fall into one of three categories: university sponsorship, industrial sponsorship, and professional society sponsorship. Local IEEE chapters have been good sponsors for teams in the past.
Having met you in the past during Mission 6, I know that you are an "outgoing" person, so you should have no trouble approaching people. Check out this link: http://aerospace.regionaldirectory.us/california.htm
It shows around 50 aerospace companies in California which you can approach (contact info provided at this link). You will have to have a slick confident presentation, but be sure to try to showcase some of their products in your entry so as you are successful, they receive some free PR.