There is a shuttle at Seatac but it primarily goes north, it does go to Anacortes. If you wanted to start out on the Northern Tier you could ship your bikes to a motel in Anacortes and you're basically at the start. You could ride the NT to Montana and then figure out how to connect with the Trans Am in Missoula. I imagine some here have connected the two routes. I used the shuttle last summer for the Northern Tier and it was quite a bargain. Here is the link:http://www.airporter.com/
I think that a lot of people who ride the Trans Am W to E fly into Portland. Some ride from Portland to Astoria. Reading bicycling journals can be very helpful, here's a very popular site.http://www.crazyguyonabike.com/?o=RrzKj
Just do a journal search for the route you would like to ride. It can give you insight into what others have done at the beginning as well as along the route. Plus it will keep you excited while the snow is still flying in N.Y.