I hate to say this, the insurance company couldn't care less about peoples emotions and feelings
I really hope you do come out on top; but without an apprasal there going to low ball you, and if you can't really find an example of why it should be a 15,000 dollar car they'll give you that low offer, or maybe even write it off if they believe the value to fix is above payout value
hopefully you have alot of reciepts to prove its worth it for them