Yes, the credit cards do carry a higher rate. But because you pay them off more quickly you only end up paying about half as much in interest expense. There is a way to reduce that. Switch to the second mortgage and continue to make the same monthly payments as before. You'll return to a positive equity position in just 15 months.
Second mortgages work best if three conditions are met.
First, that the second mortgage doesn't hit you with an overly large origination fee. Second, you need to plan on paying off the second mortgage as quickly as possible. If you pay just the required amount each month you'll be giving away a lot of money in interest over the years. Thirdly, you'll need to have self-discipline. Just because your credit cards show a zero balance doesn't mean that you have extra credit to use.