Dear wow: I forget where I saw it, but your analsysis of "Yankee Doodle" seems entirely correct.
I don't remember the "Doddle" part, but suspect that "Doodle" just sounded better.

Here is a URL to annoy CK: http://memory.loc.gov/ammem/today/apr19.html

You have to scroll down a ways and click on underlined "Yankee Doodle".