The battle is over.
After nearly three hours on the phone with Apple the conclusion is that my credit card will not work and there is nothing they can or will do about it. Basically, I'll have to go around them somehow, link my pay pal account, use gift cards, etc. I don't think I'll be using any of those options.
I was really angry at first. I plotted how I would take my silent revenge by slowly banishing all things mobile Apple from my work flow. That hurts me more than it hurts them. I believe everything happens for a reason.
What is clear to me now, is that this is an opportunity. I've spent a lot of time looking at the paid apps for the iOS platform. My iTunes account itself isn't broken and I can still get free apps. Most are probably put out by developers not dissimilar to myself and my cohorts at Raging Rickshaw. It would do me good to look for alternatives to flashy paid apps.
I think what I will do is look for free apps that can do the job of the paid apps, or close. If I find a truly nice free app, I'll put up a short review on my blog and an iTunes link. It'll give me an excuse to write on my blog, help me in my own endeavors and hopefully save me some money in the long run.
It probably isn't possible to replace all my paid apps with free ones, but it might be fun and enlightening to try.