There are many of these questions I don't know the answer to, but I'd start by contacting your regional coordinator (you and I have the same one! Susan Lawrence [ sklsumgrad at comcast dot net ], she's an amazing, extremely helpful person!) This may have been what they (above) meant by head mentor as well? I'm told they have good advice and help for teams in dire straits.
I would look into whether any of the regionals you attend have a grant program attached. You could also look into NASA's "
Sustaining Grants" .... I'll dig around some more and see what I find. Many of the sponsoring organizations that work closely with FIRST have something designed to 'rescue' teams in your situation, but I hope you can find some straight up sponsors as well.