“Thanks for all the suggestions and EconProf is right that you need to stick to your guns and keep reminding them that it was an open market arms lenght transaction along with a few comps to support.”

Ultimately this is what worked for me as well. In my situation they were only 150k above my purchase price and they ended up going down to the purchase price.

It sounds like you got a great deal on the house and as you said probably a decent compromise from the appraiser. Still, you may be able to get them to come down to the purchase price if you can find enough comparable sales evidence. Good luck.