I've got both the Shaker hymnbook that it was originally published in and the article that I mentioned earlier. The words on p.50-51 of Millennial Praises are exactly as those I posted above. There is no music.

The rest of this is will be summary of the article:
G. W. Williams, "Babylon is Fallen: The Story of a North American Hymn" _The Hymn_ Volume 44, April 1993, pp 31-35.

I have a fax of a photocopy & all words were were in shaded blocks & are extremely difficult to read.

There is no author listed in Millenial Praises. The attribution of the hymn to Richard McNemar appears to be from an article by Daniel W. Patterson in Shaker Quarterly, v.18.

The first stanza of the text appears in a manuscript of tunes from the Enfield, Conn. community & may date to as early as 1810. The original 6 verses are clearly refering to images in Revelation 17-19. "It is clear ... that McNemar knew the Revelation passage thoroughly and was closely following its pattern and its precepts." The text was reprinted in an 1833 Shaker hymnal, but not in later ones.

It was reprinted in non-Shaker books, usually with variations on words, from the 1820's on. The first verse always remains substantially the same, except for the reference to 'the distant coasts of Shinar.' Shinar did not mean much more in the 19th cent. than it does to us today. It means "Babylon in its fullest extent" and is used in the O.T. to refer to Babylon. Always associated with impiety in some way, the substitution of "courts of Zion" or "our Shiloh" substantially changes the meaning of the 2nd part of the verse. It transforms "cries of despair from the citizens of the ravished city to shouts of triumph from God's favored people."

The 3rd verse from the Sacred Harp version was first published in William Houser's "The Olive Leaf" in 1878. This was also the book where Chute's tune was first published so the version most well know now traces most directly to it. Either Houser or Chute may have written the 3rd verse, there's not really any way to know. This new verse changes the tone of the hymn to emphasizing rejoicing in triumph rather than the desolation in destruction of the original.

Before 1878 at least 2 different tunes were paired with the words in different publications. All apparently suffered from the problem that the chorus does not follow the same 8,7 meter of the verses. The 12,10 of the chorus were somehow forced into the 8,7 pattern of the tunes used.

William Houser first published a 6 verse version with one of these problem tunes in The Hesperian Harp, 1852. When Houser published it in The Olive Leaf, 1878 with the now familiar tune he headed the entry with the attribution. "Prof. Wm.E. Chute, of Ontario. Prof. composed this tune out of an old theme, and is too modest to claim any originality, but I do it for him.--W.H." The 'old theme' may be Sons of Sorrow

The author makes no mention of any versions outside of the Western Hemisphere. It seems to have been quite popular if it managed to be parodied.