Hi Lori and welcome to the forum,
As a general rule, road transport is always going to be more expensive the further they have to transport the load, however, there can be exceptions to that rule. Back-loading is a term used when the transporter has some left over space they are looking to fill, that can get you a cheaper rate, but you have to of course work in with the transporter as to when they have that space available, so not always practical.
Another option is to find a transporter either from your area doing a run to the east coast and back, they will usually be looking to find some load to bring back home way so they aren't running one way completely empty. Again, you have to work to the trucking companies time frame, so again perhaps not very practical unfortunately.
Still, it never hurts to chase up a few transporters when you are ready to ship, you may well get lucky and find one of those options available to you at the time.
I would suggest listing the pick-up on a site like uShip.com, that puts your job out to tender and then all sorts of transporters get to see it and can post a bid on your job. That's a good option because you never know who sees a listing like that, might even be a family moving cross country with some space in the trailer, maybe a car transporter dropping off a car on the East Coast and heading back home West.
There will be transport options out there that will boggle your mind, so it's always worthy throwing it out there and see what options come up at the time.
Cheers