I shipped my car from Vancouver to Montreal last summer. I used Hansen's Shipping.
LHF Vehicle Shipping, Car Shipping, Auto Transport - Welcome
Cost was covered by my company, but the bill was a hair over $1500 including taxes. Car was picked up at my parent's house and dropped off in front of my house in Montreal. Car was covered while in transport (rail).
As for why your car will be valued less, it's because it's an East coast car that goes through actual winter conditions and all the salt on the roads.