You could try telling them you don't want the money and you don't believe you can replace it for that price....so ask them to replace the car. I doubt they'll find one for $2,000.
I would go the appraisal route first though. See, it really depends if you're negotitating with your insurance company or the other drivers insurance company. You have more leverage over the other drivers insurance.
I had a door hit in my 1978 formula. The car was parked on a street where my daughter was babysitting. The guy across the street backed out of his driveway and hit my door. He said my daughter was a fault....go figure that one! His insurance company tried to total my formula. I laughed at them and said they were going to fix it one way or the other. They came out to the house expecting to see a 1978 rust bucket, but instead saw a pristine car that looked like it just rolled off the assembly line. They fixed the door to the tune of over $3,000.....yep $3,000 to fix a dented in door....after all it is California! But the job was perfect. I was impressed and I'm not easily impressed when it comes to body work.