MIDI & lyrics of the 1859 edition are at Public Domain Music (scroll down to "1859").

A college song version, which is in The Most Popular College Songs (Hinds, Hayden & Eldredge, 1904; rev. ed., 1906, p. 17; "The Quilting Party") and in Carmina Princetona: The Princeton Song Book (G. Schirmer, 1902; 21th ed., 1927, p. 98; "Aunt Dinah's Quilting Party"), has the familiar tune & words.

The Virtual Gramophone has this recording: "Aunt Dinah's quilting party, or, Seeing Nellie home -- Haydn Quartet" (Recorded: [10 Sep 1903], Camden, NJ by Victor Talking Machine), which also has the "rested light as ocean foam" stanza.

These editions (without music) are at Bodleian Library Broadside Ballads:

When I Saw Sweet Nelly Home

Seeing Nelly Home

Floyd County Ramblers' "Aunt Dinah's Quilting Party" is on Times Ain't Like They Used To Be, Vol. 6: Classic Recordings of the 1920s and 30s (Yazoo 2064) and on Black & White Hillbilly Music: Early Harmonica Recordings from the 1920s & 1930s (Trikont 226) [both with sound clip].