In a truck, it will probably take you a little more than 20 hours, FYI. It took us 20 in our car to Seattle from Denver. Are you stopping for a night? (We didn't).
Let me know if you need any local help!
We always said if we were moving that far away that my husband would drive and get there and set up, then I would fly out with the animals.
Frontier and Southwest have been having some pretty good deals ($60 one way) to Seattle that would cut your 2 day fiasco into an afternoon, not sure about animals regs with them though...
Oh, and I am SO jealous that you're moving to Seattle, I LOVE that place, but am too much of a sun worshiper to move there.
Good Luck!!!