I think you need to get a Dave Ramsey book (or Financial Peace Univ) and follow the debt snowball. I think if you start with Chase Freedom, pay it off, then move to Amex, and continue upwards you'll start making quick headway and will feel better. A lot of your stress is the overwhelmed feeling, but if you start to pay off cards relatively quickly (even if they are the small ones) psychologically you'll feel better and will be motivated to stick with it.
I'm also not sure BK is a viable option as the trustee may see private school as a luxury and make you use that money to pay creditors anyway. So now you've filed BK, destroyed your credit, burnt bridges with creditors who may never let you back in and your kids still aren't in private school. Oh, not to mention the cost to file BK is around $2000.
Good luck!
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