The Revivalist by Joseph Hillman was published in 1868 and 1872 (according to George Pullen Jackson).

In the Print Bibliography at Patriotic Melodies (Library of Congress) (linked to above by Q), there is Katherine Little Bakeless's Glory, hallelujah! The story of the Battle hymn of the republic (Philadelphia and New York: J. B. Lippincott Company, 1944). The author, however, does not believe Steffe composed the tune, saying that:

    This hymn ["Say, Brothers, Will you Meet Us?"] may be found in an old hymn book of 1860, called the Sabbath School Bell, but no author's name is given. There is the acknowledgment that it was taken from the "'LEE AVENUE CASKET.' By permission," and "arranged" by Frank H. Lummus.
    [part of score quoted]
    This "arrangement," which uses a more even, calm rhythm (introduced by the words), does not ask for the rousing march tempo that swings along John Brown's Body.
    Except for this story, Steffe's name seems to have been forgotten, for there appears to be no record of his having written any other tunes. This hymn is supposed to have appeared in a hymn book called The Lee Avenue Collection, Part 2, No. 208, compiled by Jeremiah Johnson, Jr., "about" 1858, and to have been first printed in The Lee Avenue Sunday School Casket, Vol. 1, No. 152, "before" 1858.

Bakeless suggested Thomas Bingham Bishop composed it throughout the book.