Personal Opinion: I am in the same situation, except my house is not entirely paid for. What I was told by a financial councelor was to get a personal loan to cover my high interest CC debt. Hopefully, the personal will have a lower interest rate. So, in a sense, I combine my total CC debt into One lump sum, and pay it back at a lower interest rate, plus I have a smaller payout each month. Which can be altered to pay off the debt faster.
One factor about the Home Equity Loan is that, if you fail to pay it off, you risk losing your home. Its possible to lose a 160,000 dollar home on a 30,000 dollar equity loan because the bank want's it money back, and your home is the collateral. But, a Home equity loan is the easiest easy to get since you have your house paid off.
The biggest factor in paying off all your cc debt at one time is you erase your credit history. This being the Second item looked at when calculating your all important Credit Score. If you have no history, you end up with a very low Credit Score, which costs you money in the end. Its best to pay off everything except one card. So you keep that history going.
P.S.: Number One, when calculating your Credit Score, is Derogatory statments you make to bill collectors, and number three is having more than 33% of your total debt on one particular card. both will lower your score dramatically.
Hope this info helps. Cheers!