Solution

It is amazing how little home ownership knowledge I have, I need to remedy that. K researched about home equity lines of credit and found that could be a solution for us. We spent two hours at the bank yesterday to only be denied in the end because her length of credit history wasn't long enough and she was maxed out on her available credit.

In the end, we will still need her dad to cosign on the line of credit (which he agreed to do and they will be closing on it Friday). This is probably the best solution that could have happened. We are getting out from under $30K in credit cards and the interest rate is only 3.49% compared to almost 30% we were paying. He still pushed the roommate idea to pay them off even faster, but K finally convinced him that it was unnecessary due to how much we are already committing to pay monthly. 

Still sucks to have parental involvement but, it is a better outcome than I had envisioned on Tuesday.