I have some questions, as the story doesn't at present tie together quite right.
First, about this statement:
"Ragnar T. Thillesen lived with his grandmother, Mathea Thillesen, until he emigrated to Canada...1927. On the 8. Nov 1937 he came to New Orleans, Louisiana, on his way to visit his father Thille T. Thillesen."
Did Ragnar emigrate to Canada (settle there)- do you know from family stories he lived in Canada from 1927 onward?
Or did you find a record that he sailed to Canada and entered North America at a Canadian port in 1927? If the latter, he might have gone to California from his port of arrival in Canada.
As far as we know, when in Canada, Ragnar lived in British Columbia, due north of California. He would not travel in 1937 from British Columbia to New Orleans, Louisiana, to get to his father's home in California!
It may be Ragnar came to British Columbia AFTER the 1937 voyage and had lived in eastern Canada prior to that? Or had returned to Norway for a stay or a visit? And returned via New Orleans? (which still makes little sense, as more likely he would have traveled via the Great Lakes, and then by train, like everybody else).
In 1929, the child Thille claims on his naturalization papers is "Raynar." Are you guessing, tester 1887, this might mean Ragnar?
Understand, I'm not disputing the facts here - mostly just the narrative about the arrival in New Orleans.