The version in the DT under the title "We Are Climbing Jacob's Ladder" seems to be a combination of the version in Dett and one by Seeger. Here is the one from Dett:

WE ARE CLIMBING JACOB'S LADDER

We are climbing Jacob's ladder (3x)
Soldier of the cross.

Every round goes higher and higher, (3x)
Soldier of the cross.

Sinner, do you love my Jesus? (3x)
Soldier of the cross.

If you love Him, why not serve Him? (3x)
Soldier of the cross.

Do you think I'd make a soldier? (3x)
Soldier of the cross.

We are climbing higher and higher, (3x)
Soldier of the cross.

R. Nathaniel Dett, ed., 1927, "Religious Folk-Songs of the Negro as Sung at the Hampton Institute," p. 118, with music.
Note: Not certain when this was added to the Hampton song book. It is not in Fenner's 1874 initial publication. Probably added in the 1909 edition when twenty-five new songs were contributed by Work and others.