I used to work as a shagger (someone who drives cars out of Mazda final assembly to be loaded onto truck and rail) and I can't recomend a sort of broken vehicle getting to you safely by rail. We were not easy on vehicles coming from Japan that came into our midwest hub for unloading by rail. 9 vehicles(on average) a year "somehow" jumped the ramps to only land totaled on the concrete. 90% of the time it was the Miata's and Protege's...
Anyway, I'd call dealers in your area to see if they have logistic routes to and from seattle. Ya know, shmooze with them...Maybe they would pickup your car on one of thier delivery backhauls?
This company, Cassens Transport, has in the past. 600 mile trip, $300.
They did it for my friend, and here is thier website
Cassens Transport
...then again, Rail may be your "cheapest" option being that 1000miles is involved.
P.S.~I'd bet $500 bucks that ANY car haulin trucker picking up your vehicle could safely get that rear wheel unstuck. Those friggin guys are a different brand of human, and they can do things with a vehicle that would leave you speechless. (Including the driving manuevers they can perform if need be!)