Wayfaring Stranger - The song appears under the title I'm a Pilgrim, No. 45 on p. 43, in The Southern Zion's Songster, 1864, Raleigh, NC.

First verse and chorus:
I'm a pilgrim and I'm a stranger,
I can tarry but a night,
Do not detain me, for I am going,
To where the fountains are ever flowing.

There the glory is ever shining!
O, my longing heart, my longing heart is there,
Here in this country so dark and dreary,
I long have wandered forlorn and weary.

I'm a pilgrim, etc.

There's the city to which I journey;
My Redeemer, my redeemer is its light,
There is no sorrow nor any sighing,
Nor any tears there, nor any dying.

I'm a pilgrim, etc.

Farewell, dreary earth, by sin so blighted,
In immortal beauty soon you'll be arrayed!
He who has formed thee will soon restore thee!
And then thy dread curse shall never more be.

I'm a pilgrim, etc.

Note that there is no chorus about going over Jordan; I'm a pilgrim and a stranger is the 1st line of the chorus here. The references are indeed confusing. The Sacred Harp 1844 reference in the ballad Index, Univ. California-Fresno is probably an error.
The Southern Zion's Songster is reproduced in its entirety on the Univ. North Carolina website http//docsouth.unc.edu/imls/zion/zion.html