Heh. I'm a electronics guy who was the build lead last year and is the build lead this year. The team always pushes for a strategy that is way more complicated than it has to be, but I have been able to manage nonetheless. How do I do it?
I never forget that I have to push myself no matter what, that FIRST is about more than just the students. If there is something that must be learned, I will learn it (like CAD). If there are industry standards to be met when interfacing with people who work with us, I will meet them (such as CAD drawings). Leaders need big shoulders to carry the weight when it's needed. When no one knows what to do on a subject, I try to come up with a first pass at it. I know that everyone will sit and pick it apart and say 'X should be Y', yet the reality is none of them were willing to put up a draft to start prototyping with. Then I, the other build mentor, and our best mechanical students prototype and finalize the design. Literally, we never fail for lack of effort on the team so long as each team member tries.
During the season, I just take it a day at a time (with some planning ahead of course).
My biggest tip: know your teammate's interests, and play to their interests and strengths rather than your own. Yea, that's right...your ideas may be ignored for a while, but the best ideas usually pull through anyways. That's the only way we've kept our head above water these last 2 years.
If you really feel strongly about something and need to inspire them to view a design (concept, idea, or otherwise) your way, a picture or video is the best piece of incontrovertible evidence that you can present to them. The next best thing is math that proves your point and is explainable but looks like it goes over their heads
(haha, usually they look at the answer once and are speechless)...though a good engineer won't trust your math until they've done it themselves.
Good luck this season. Prove your mentors wrong (but in a tactful way)...the reality is they will respect you twice as much when you do.