This may not be the answer you wanted to hear. but here is a quick analysis.
You have a lifestyle problem. The reason you went from living "phat" to "flat" is that you bought a whole bunch of junk on credit because you couldn't afford to pay for it with cash. In translation, you've been living beyond your means for the last 6 months; it's just taken this long for it to catch up with you and you to come to the realization that you have to find some way to pay for all this.
There is a fundamental problem with taking equity out of your home to pay the bills in your situation. In 6 months, you managed to build $15k in credit card debt. If you pull $15k of equity out of your home, you can pay the credit cards off (nevermind the fact that you'll be paying it off over 30 years or however long the loan terms call for). The problem is that if you don't change the way you handle your money (see paragraph #2), in 6 months you'll be back int he same boat: a bunch of credit card debt and no way to pay for it except to pull more equity out of your home. That works fine once, or maybe even twice. However, it's a losing plan in the long term because you'll eventually have no more equity to pull out and you'll be stuck with the credit debt AND the increased mortgage payments.
If you take the equity in your home and turn that into cash to pay off the credit card debt, you really need to cut up those credit cards, close accounts, and vow to not use credit cards again. If you don't change these habits, you will find yourself in this situation again down the road, and someone, be it AmEx or the mortgage company, is going to continue to "own your azzes" for a very long time.