I don't think the OP should necessarily sell the 19.4K car.
My reason is, the 19.4K car with 0% interest is most likely a newer car, and will provide 10 plus years of service.
In order to make it worth his while, he'd need to get a car for 10k or less. And that puts you in 2009 Kia Rio territory. No one should suffer so much to drive one of those.
If the OP trades the 19.4K car in, he might be lucky to get 16K trade in...
End of the day, save a few thousand dollars getting an older car, that is going to need to be replaced sooner. End result, probably spending more money in the long run.
I've grappled with this myself. Currently I have a 15K car loan, on a really nice car. I've considered downgrading my ride and having no payment. Test driven countless cars, wasted a lot of salesman's time, ran the numbers at home. My insurance would go down, save a little bit on gas and tires. But at the end of the day, my car is going to have a much better resale value in five years or even ten years than a 2009 Kia Rio, Hyundai Accent, or Chevy Cobalt.
Last but not least, if the OP really likes his car, there is the potential of seller's remorse. At least for me in my scenario, that has ran pretty strongly through my head on every car I've driven. Is the money I might "potentially" save worth trading down to an economy car in the big picture?