One aspect of Huckleberry Finn (the novel) that I think is relevant today is the spectacularly stupid zero-sum conflict between the Grangerfords and the Shepherdsons. It seems relevant to the US's politics and many international conflicts
For books you have "The Innocents Abroad", "Roughing It", "The Adventures of Tom Sawyer", "A Tramp Abroad", "The Prince and the Pauper", "Life on the Mississippi", "Adventures of Huckleberry Finn", and "A Connecticut Yankee in King Arthur’s Court".
That's a hell of a lineup and includes a LOT of the flavor of the US as a young country.
I would agree with other posters that if we allow the search to stretch into the 20th century, odds are we'd end up with a filmmaker or songwriter, but I think we've got our all-around best options already, and they're all (basically) 19th century.
Also the American Homer is/was Garrison Keillor. Homer’s delivery was oral and radio is surely closer to oratory than books.
I think high school readings are quite pointless in general, because most kids either aren't mentally developed enough, or aren't going to have the focus, to actually "get" what's being said - at least not beyond the point of cramming enough stuff down to be able to puke it back up on a test/report.
That was certainly the case for me and I think this is extremely common given there are plenty of people that think Huck Finn is a racist book, when the entire underlying message is a never-ending mockery of racism.
I've gone back and read so many books I was supposed to have read in HS and college. I don't think at the time I had the life experience to fully grasp many of the message(s). It's one thing for a teacher or guide to explain in abstract the underlying messages, it's another to have dealt with them in your own life and see yourself in the characters [1].
[1] I always read like I'm one or more of the characters and not simply an observer.
Though other American countries (even just North American countries) might have different opinions, so maybe he's just the USA's Homer.