Canadian experience here, and possibly not money smart.
You can sell a car you have a loan on. What you do is take out a personal line of credit (unsecured) equal in value to the car loan - in this case $2000. Pay off the loan with the PLC.
Apply for a 0% for 90 days Mastercard for $10,000 Pay off the loan with the mastercard. There is no charge to consolidate loans to the card, and the PLC allows you flexibility to buy time to move the loan over. If you are smart you will find a Mastercard with some kind of bonus miles or whatever.
Sell the car. Pay down the Mastercard with proceeds of sale. You now have 80 days to find the outstanding cash. If you fail, move it back to the PLC at 3% and continue to pay it down.