Check and see which Amtrak stations permit entry and exit of bikes and/or boxed bikes/freight. Don't believe all of them do, and even the ones that do may have day/date/train restrictions, which may significantly reduce your options at each end.

At one point I believe that Amtrak actually supplied 'bike carriers' which retained the bike fully assembled so that it could be strapped to the inside of the freight car. Check on that.