I am guessing not knowing all the facts that refinance will not work by the time you factor cost setting up a new loan, also with the term and interest rate at time of purchase I have a strong feeling you may be up - side down.
If you want let's do the math,,, phone the lender for a payout amount ??? e-mail to keep it private along with your zip code, model Accord and miles, or post it your choice.
up - side down is if your payout is greater than what you can sell for.
If your happy with your 06 personally I would not trade up just 2 or 3 years owing 11G,,, I would however investigate getting a lower rate on the amount owed " credit union or your bank,,, it really comes down to compare the final numbers if it's feasible.
You can also get a fast free on this website, under navigation on the left side, click on " facts to consider before going shopping "scroll down to " research your auto financing options,,, and click on get an auto loan quote now,,, I been associated with Automotive.com for a few years and have never had any negative feedback.
I will be interested to know the rate quoted.