We made our cross country moving using Amtrak to ship a lot of boxes.
https://www.amtrak.com/express-shipping
How I moved across the country with Amtrak - Transitized
This is how it went for us:
Boxed everything up in the small heavy duty Lowe's moving boxes.
Drove to Cincinnati's Union Terminal after hours(for that location was the only time they accepted shipments as it was also a museum and such)
Went and chatted with the guy on duty who gave us a couple carts to load up the shipment.
He weighed and processed each package then they were set out to be palletized.
We then took off on our cross country drive to Portland. The train beat us there by a day. But they hold the shipment for 72hrs before they start charging you for storage.
Got there, got keys to our place then went down to the Portland terminal and got our boxes.
They all got dirty, but were in great shape otherwise.
Was the cheapest shipping option by far. I see they say that bikes must be boxed and that they may have said boxes available but to call ahead. Also you cannot ship electronics with them so those need to go with you or be shipped in another way.