Art,
Your mind is still sharp as a tack. "RedRiver Shore" is indeed in Folk Songs of North America, AND it does contain the verse that you include! Furthermore in that book it is listed as being on p 298 of Cowboy Songs. The only slip is that it is the 1938 edition of Cowboy Songs which was somewhat revised and expanded from the 1910 edition. You can relax now.
rich r