I went to the DT to look up the lyrics to this old spiritual. I concluded that something wasn't right when I got to the second verse and noticed that "Steep and rough" did not rhyme with "no more shall weep." So I went looking for another source.

Lift Every Voice and Sing II is a hymnal published by the Episcopal Church featuring all-African-American material. Here's the lyrics found there. (Changing "steep and rough" to "rough and steep" saves that rhyme in verse two, obviously enough. The differences between the DT and LEVAS versions are greater in each successive verse ~ the four and final verses of the two versions are completely different:

I am a poor wayfaring stranger
Traveling through this land of woe
And there's no sickness, toil or danger
In that bright world to which I go

I'm going home to see my father, I'm going there no more to roam
I'm just a going over Jordan; I'm just a-going over home.
        
I know dark clouds will gather round me
I know my way is rough and steep
But golden fields lie just beyond me
Where weary eyes no more shall weep

I'm going home to see my mother, I'm going there no more to roam
I'm just a going over Jordan; I'm just a-going over home.

I want to shout Salvation's glory
In concert with the blood-washed band
I want to wear a crown of glory
When I get home to that bright land

I'm going home to see my brothers, I'm going there no more to roam
I'm just a going over Jordan; I'm just a-going over home.

I'll soon be free from every trial
This form will rest beneath the sod
I'll drop the cross of self-denial
And enter in my home with God

I'm going there to see my Savior, Who shed for me His precious blood
I'm just a going over Jordan; I'm just a-going over home.