I assume that the board members are volunteers so it is unlikely that you would have an employment discrimination case on the basis of age or any other protected characteristic.

You might have legal recourse for an improper election as a matter of state nonprofit corporate law, but your only real chance to be elected seems to be (if you can’t convince the board to nominate you next year) to get the 10% petition nomination and then campaign to win.  Test the waters with the other members and tell them about your experience with the current administration.  Tell them about your “fresh ideas” of what you want to do as a director, not just how much you want to be a director.  You may find that others are as offended by the current administration as you are and supportive of your effort.  You may also find that no one else cares.

If you can’t get enough to sign your petition and don’t have an indication that there might be more support for your candidacy out there, there is no reason to spend the time and money to seek to undo an election or run a campaign next year when you wouldn’t be able to win anyway.  You could continue as a gadfly to the current board and could run a perpetual campaign to get the signatures necessary to run.  But if you don’t have success securing a following, you probably have a lot better ways to spend your time and energy.