We ended up using Amtrak Express Shipping (
Amtrak - Plan - Planning & Booking - Baggage & Shipping - Amtrak Express Shipping), to ship boxes whose weight totaled approximately 600 pounds. The rate per pound decreases progressively, depending on how much your shipment weighs. However the rates were VERY reasonable in comparison to the competition. (After a certain point, it cost .56 per pound to ship from NC to CA.)
One thing to be aware of before showing up with your boxes at your local Amtrak station is that shipping is an add-on to Amtrak's core mission of transporting people. So, if you arrive just prior to a passenger train's arrival, staff might not be able to help you. Also, you must be very careful not to exceed the 50 pd. limit for each box, because staff must load and unload the boxes oftentimes without forklifts, etc.