I am the sponsor/coach for our team and I think you may be looking in the wrong direction. I teach Introduction to Computers, Computer Maintenance, and Networking (which falls under the Career and Technology department).
We do not recruit from "specific" groups or classes we have an open door policy for everyone on campus. I have had students who can work cal2 and phys2 equations all day long that have never picked up a screwdriver and at the same time I have had students who couldn't tell you what a phys equation was but if you handed them a part they could have it assembled and working in less than 30 minutes and be able to tell you if it could pick up a 7.5lb, 40in diameter ball.
What's really cool is that these guys end up teaching each other their skills and it makes us a MUCH stronger team (stronger as getting through the tough times). The teachers that you would "expect" to be involved in this aren't (we can go ask a questions but they don't show up for meetings etc.) and we are having fun figuring out the answers to our questions on our own and being successful!
My advice to you...if you have a career and technology department at your school go talk to them if you haven't already! They LOVE to get their hands on stuff like this (I sometimes have trouble keeping my fellow CTE teachers from trying to build it for the team!) The welding instructor is checking in with me at LEAST once a week to see if we need any help or if there's anything they can weld for us yet.
Remeber, talent can be found in VERY unexpected places! Check out this link if you don't believe me
http://www.snopes.com/music/artists/bell.asp
Most of all, keep your heads up and keep fighting for your team...it will be worth it in the end!
Good luck at competition!