What if you just stopped paying the CCs and pile up cash? Your credit would be wrecked either way but now you can negotiate with the CC companies.

You call them up one by one as you have some cash and offer them, say 50% or 25%, and if they refuse, tell them you are moving on to the next CC. You'll get back to them when you have some cash again. Rinse and repeat.

It won't be easy, and will take time. But it could work.

BTW, you have too much house unless your wife and you double your income.