Hello Carol,
I can see what you mean about the warship dominating the articles. There’s not much around for the civilian model.
Looks like the company had a few variations in its name: Hamburg-Amerikanische, Hamburg-Amerika and Hamburg-American etc.
According to
http://www.theshipslist.com/ships/lines/hamburg.html the Hessen, 8,116 tons, was owned by them 1921 to 1935 when it was sold to Unterweser, Bremen, and renamed Fechenheim.
12 Feb, 1943, Russian submarine K-3 torpedoes and heavily damages the German merchant Fechenheim (8116 GRT) off the Batsfjord. The Fechenheim is beached to prevent sinking. Later the ship is salvaged and towed back to Germany but she was deemed beyond repair.
http://www.uboat.net/allies/warships/ship/5125.html
A search for hessen under the advertising category 1920-1936 in the London Times brought up a couple, Monday, Aug 01 and 15th, 1927, regarding the Hamburg-Amerika Linie - Hessen leaving Rotterdam Aug 17 1927, calling at Japan etc.
I think this page has all you need including a photo but I don’t speak German.
http://www.schiffe-maxim.de/Hessen.htm
How’s that,
Alan