Send them $10.00 a month. As long as you are paying something there is nothing they can do except charge you penalties. Just plan on paying the rest of your life, but even if you love another 100 years it is only $12000.00.
As for screwing over a credit card company by delcaring you are bankrupt, who cares. Lets not forget they are owned by banks who received a bailout, and are not charged any interest, yet have no problem charging you 29% interest. Who exactly is screwing who?