If you have good credit, try this..
Look up the Neon, on KBB.Com, and put it up for sale, LOCALLY for the "private party" price...
Go to a bank, and see if you can get an unsecured loan for the balance due. If you can.
You can also, take the plates off of the Neon, let it sit, with just comprehensive insurance on it, that will save a huge amount of insurance money, but if you do this, be certain to call the loan holder and explain why you are doing it...as long as it has comprehensive insurance on it, they will allow it.
If you manage to get a loan for the difference, and sell it, you will still have a payment, abet a much smaller one for awhile..
This is one of those situations, where life just is not fair.