Thank you for the link to the "I am a Pilgrim" thread, Joe Offer. Despite a few similarities, they are different hymns.
1. "I am a poor wayfaring stranger"
a. Second line: "I'm traveling through this world of woe."
b. Refrain "I'm just going over Jordan."
c. Appearance: Words only at p. 34 of Joseph Bever, "Christian Songster" (Dayton, Ohio: United Brethren in Christ 1858)
2. "I am a pilgrim and I'm a stranger."
a. Second line: "I can tarry but a night."
b. Refrain: same as first and second lines.
c. Appearance: Mary S.B. Dana (author of the lyrics), "The Northern Harp" (NY: Dayton & Saxon 1841), set at p. 54 to an "Italian Melody" which is different than the tune used for "I am a poor wayfaring stranger."
As the other thread notes, Mrs. Dana's hymn was quite popular, being reprinted in 1848, 1854, 1855, in three Civil War soldier hymnals and in numerous postwar hymnals. It has also appeared to additional tunes, but of the four tunes I looked at, none match the one for "I am a poor Wayfaring Stranger."
So, I'm still in the dark about the earliest publication of "I am a poor wayfaring stranger" with the tune we use.