Here are my thoughts on this...
As a student, you shouldn't be starting an FRC team by yourself. Instead, inspire an existing organization, such as a local school, business, or the university to embrace FIRST and its vision. Use this to start an FIRST
program. Build the foundation for the program to succeed, so that even after you've graduated, it will succeed.
By working the sponsorship, facilities planning, team structure, and "boring mentor stuff", you will lay the path for a bright future. Plan the organization so it can operate without you.
I'm not sure where you plan to take your future. You may leave the area just as the team starts to "norm", where the start-up kinks are worked out and everyone is working together in harmony. Having the program, the plan, and the support structure in place will give the team a great shot at success in the transition. I would encourage you to find a more permanent team leader that can provide consistent leadership and mentoring through the years.
Maybe this person could be you. It is possible to work with the university to found the program, then write a job description for the program manager and hire into the school's faculty
Starting an FRC program is no easy task and looks great from an employer perspective.
As always, I know the FIRST community will lend a hand wherever is needed.