I'm not convinced you could agree to settle such an application for money. Agreeing to discontinue an application for mandamus (the kind of court order you're referring to) that was to bless you with public power and impose upon you duties you were elected to carry out in exchange for money is roughly as corrupt as trying to prevent this guy from taking office in the first place, and may well be illegal. But "the town settles" in a broader sense of "agrees to stand down and swear you in", yes. Also nitpick, you would sue the individual members of the Board in their official capacity.