There are no direct trains between Hamburg and Copenhagen and vice versa from 23 March to 04 June 2018 – so unfortunately the eccentric train on a ship won’t happen!
Read my impressions of travelling across the United States on @amtrak trains. There is no better way to discover America - and the American people, given that you're almost forced to interact with them at the shared tables of the dining car - than riding an Amtrak train.