Wow. The scenario you describe boggles the mind. Truly.
Our system is simple and easy. The core members just work, and when we need help with something we ask whoever isn't doing anything. You don't help, you get the evil eye from everyone and you probably are motivated to do better, but if not you'll probably feel so socially awkward you won't show up again. You do help and we try to teach you.
The hope is that eventually these non-core members will have become proficient enough to start their own project, at which point the "circle of robotics" (ala Lion King) continues
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Too many members is an interesting problem. I'd make cuts based on
semester Grade Point Average (or the brazillian equivalent, but absolutely NOT cumulative grade point average, as that would be totally unfair). This would have the pleasant side effect of motivating students to work harder in school. You have a set number of people you want on the team each year, then you order all the applicants by GPA and go down the list adding people to the team. If someone doesn't pull their weight, they are kicked out for that season and replaced with the next applicant on the list. I'm sure teachers would love you for motivating students.