Here is some possible evidence that the use of the term "ship" for airplane was common in the mid-1930s.
American Airlines and the Douglas Aircraft Company, recognizing the potential of the film in advertising air travel, cooperated in the production and distribution. They provided a DC-2 aircraft for the exterior shots while a true to scale mock up was provided for the interior scenes. In the famous Good Ship Lollipop scene, members of the University of Southern California football team served as extras.
I agree with you it's possible.
I'm still not entirely convinced.
You're claiming the man on the street at the time would find the word 'ship' interchangeable in meaning between ship at sea and aircraft.
There are a lot of very sophisticated lyrics at the time but I'm not certain how many represent the vernacular.
I see figures of around 500,000 in annual ticket sales for U.S. airlines in the early 1930s (Source: Daniel Rust, Flying Across America, Univ. Oklahoma, 2012, p. 92.)
That's less than 1/2 of 1 percent of the U.S. population at that time. To most Americans in 1937, a trip by air should have been as exotic as, say, a trip to Niku. Note that regular airline passenger service had only existed for about 11 years in 1937. In my experience, people settle on new meanings for old words when they've experienced something at least a few times.
In my view, 16-year-old Dana Randolph's alleged hearing of the phrase "ship is on a reef south of the equator" on his radio is nearly - but not quite - on par with Betty's hearing "get the suitcase in my closet" or "watch that battery."
I wonder if use of the word 'ship' was part of the general push by the airline industry itself, and cooperating aviators such as Lindbergh and Earhart, to try to impress upon the public that airplanes were as safe as ships. Recall Earhart said in her first book, 20 Hours, 40 Minutes, "I can only hope that ... some of the charm and romance of old ships may be seen to cling similarly to the ships of the air." Earhart was someone with a keen interest in promoting air commerce in the passenger realm. Your mention of the cooperation of the air industry in promoting the Shirley Temple film is possible evidence of this as well.
I could be wrong about all of this, or reeling off facts to feel more comfortable in my opinions. But something seems a bit too easy to me to assume that people defining ship in 1937 would instantly reach for the word airplane. I'm sure many knew it could mean that. But how many really embraced that meaning?
There's probably no right answer in all this. I'm just introducing new things to ponder and appreciate your taking time to ponder it as well.
Joe Cerniglia