One possible other option, other than resigning, is to begin agitating for openness in Government. Unless are talking about actual mobster guys, you could simply say "I believe that we owe it to our constituents to ensure that they know exactly what it is we are doing with their money, and on our dime. I believe our meetings should be recorded, and that we should discuss none of our local governments business outside of a public forum. There is no need for it, and there is every need for our citizens to be confident that our Government is working for them, in an open and forthright way."

Bringing it up publicly in that matter might well make headway. Even if the corruptorinos squash it, it can become a campaign issue for method B.

Bryant