Home in that Rock- God Gave Noah the Rainbow Sign discussed with texts and references in thread 40983: I Got a Home

Agreed, "Anchored in Love" is original title of the James D. Vaughan-James Rowe song; 1911. Words from Vaughan book, "Crowning Phrases."
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Perhaps the best way is to approach their tunes alphabetically, so that some organization can be given to this list.

Amber Tresses (tied in blue)- "Amber Tresses Tied in Blue," 1874. Words by Samuel M. Mitchell, music by H. P. Danks. Sheet music at Levy. (Posted above by Malcolm)

Angel Band- "My Latest Sun Is Sinking Fast," c. 1862. Words by Jefferson Hascall, music by William B. Bradbury, in Golden Shower, 1862. Text in Cyberhymnal.
Cho.
O come, angel band,
Come and around me stand,
O bear me away on your snowy wings,
etc....
(There are other 'Angel Bands', but the chorus is the right one.

Answer to Weeping Willow- Or how morbid can you get). Didn't find it.

Are You Lonesome Tonight - "Are You Lonesome To-night? 1926. Lyrics Roy Turk, music Lou Hindman. Henry Burr made it famous. Copied by Elvis. Hmmm, did the Carters pay royalties or were they different enough?