Here's a very nice finger-picking arrangement for dulcimer from YouTube. Look at the guy's left hand, he's playing in the Dorian mode.
[YouTube:] I Will Arise - Mountain Dulcimer
Uploaded by unionshroomer on Dec 31, 2008 - I Will Arise & Poor Wayfaring Stranger medley on the Mountain Dulcimer. The dulcimer is a McSpadden Schnaufer Model.
The version of "I Will Arise" in the Sacred Harp is titled Restoration (312b). It combines Robert Robertson's 1758 text:
Come, Thou Fount of ev’ry blessing,... with the wandering chorus:
Tune my heart to sing Thy grace.
Streams of mercy, never ceasing,
Call for songs of loudest praise.
I will rise and go to Jesus,Says Erbsen, longtime director of the Appalachian music program at Warren Wilson College in Swannanoa, N.C.:
He’ll embrace me in His arms;
In the arms of my dear Savior;
Oh there are ten thousand charms.
The melody of I Will Arise has been popular in the South for over 150 years. Pieces of the tune have been found in [George Pullen] Jackson's "Spiritual Folk Songs of Early America" (p/ 233) uder such titles as Humble Penitent, Hayden, Bozrah, and New Orleans. Fragments of the tune have also appeared in secular songs like The Bird Song, Oh Love It is a Killing Thing, and When I First Left Old Ireland.Erbsen notes that the first verse ("Come Thou Fount ...") is also a floating verse that appears in Nettleton, Olney and Palms of Victory. (I knew about the first two but not the other.) His book is one of the best I've seen for old-time gospel, BTW, and he has a CD with a dozen selections from it. Most of them are too late for our period at New Salem, but one is a lovely duet on "I Will Arise" with Erbsen singing melody and Laura Boosinger of Asheville, N.C., singing alto harmony.
Another scholar of religious folk songs, Annabell Morris Buchanan, has found evidence that the melody of I Will Arise is a descendent of a Scottish tune named Hynde Horn which dates back to the 13th century or earlier.
Edgar Lee Masters' reminiscences about growing up in Petersburg are from a later period than ours -- he was born in 1868 and wrote the book in 1942 -- but they are valuable because he knew people who had lived in New Salem, more often their children, and had much to say about Menard County and the "deserted village" on the hill above the Rutledge mill site. He attended the Concord Cumberland Presbyterian Church in the Sand Ridge country north of Petersburg, and remembered the singing there:
There was no organ in the church, the audience following some song leader. They sang "There Is a Fountain Filled with Blood" and a hymn entitled "I Will Arise: based on the parable of the Prodigal Son.  Through the courtesy of Mrs. D.B. Finney, and Miss Nell Carver of Petersburg, I am able to reproduce here the musical score.Which is as good an example as anything I've read how oral transmission works.
pix These words give no idea of their moving quality when accompanied by the msuic, nor how they tugged at my heart in that longago when those simple people raised their voices in a kind of pastoral sorrow as they sang them. "Buddy" Traylor, a descedndant of the Sandridge Taylors, sings this hymn as he drives his taxi about Petersburg. But he has improved upon the wors. Insead of "He will embrace me in His arms," he sings "He will take me in His  arms"; and instead of the wrods "Oh, there are ten thousand charms," he sings, "Oh, I find ten thousand charms."
Masters also says, of the Concord church:
If there was a culture, a spiritual flowering and grown in the Sangamon River country it was among these Cumberland Presbyterians, these humble, generous souls, who in the days of Andrew Jackson followed him faithfully as their salvation from the evil plots of cities, from the schemes of selfish money-changers. They read the Psalms and the poetry of the Bible, and they sang the hymns of Watts and the Wesleys. Like primite Chrisitans they stood for moral virtue, good will, as the means of accomplishing what they regarded as the supreme object of life, the eternal salvation of the soul. Truthtelling, honest dealing, neighborly kindness were their religion. ...As always with Masters, we may be learning more about Edgar Lee Masters here than the subject at hand, but what he's saying here rings true with what I read in the county histories and other reminiscences of central Illinois in the 19th century. The Sangamon was part of the "Rivers of America" series, but it's more of an elegy than anything else. Even so, I am inclined to trust it ... in much the same way I trust Carl Sandburg to get at the poetry of life in 19th- and early 20th-century Illinois even if some of the details may not always be 100 percent reliable.
There's poetry in The Sangamon, too. For example this passage, also riffing off of Concord church:
O Orphics, Orphics of the Illinois Prairies,This is as good a description of an old-fashioned country bass as I've read anywhere.
Of Goodpasures, Clarys!
O voice of Royal Potter, whose thundering tones
Overflowed the church as a goblet which brims,
In singing the hymns
In deep crescendoes and quavering whims!
O Royal Potter, O Royal Potter
What has become of your venerable skull,
Your resurrection bones,
Your judgment day bones and skull? (128)