Re: about Aunt Rhody's Goose: Call it the "folk process" (helped along, perhaps, by the fact that this song is taught in elementary schools). I learned the lyric as:
"She died with an achin' in her head"
I suppose geese can have brain aneurisms, too....
As for John Henry: 1) it's a romantic notion in folklore to die for what you believe in, and JH believed that humanity was more important than a machine. 2) Barring romantic notions, I'd say it was a case of overblown male pride. He didn't plan on dying, but once the adreniline started mixing with the testosterone, his only thought was "winning the race", and he wasn't paying attention to the signals his body was sending him, telling him to Stop!