[Carol]

I realize that it is very easy to suggest splitting the team, but in reality money and resources can make that impossible, so I'll skip that. (Even with over 100 students you can easily tap out fundraising in an area).

If building and operating the robot is considered the "best" team, why don't you make it the ultimate goal for the students? For example, each student has to spend, say, their first year on fundraising and spirit, then their second year on Lego League, third year on BEST or VEX, then in their final year, those who stayed around and have shown the ability, can join the robot team. This of course would require a four year commitment so you may want to scale it down.