I keep running across these lyrics:
"Say, brothers, will you meet us (3x)
On Canaan's happy shore."
but it doesn't fit the tune. One more phrase is needed.

This "Say, brothers" version of the verse has the same rhythm as the "Glory, Hallelujah" chorus. Or in other words, in "Say, Brothers" the verse and the chorus have essentially identical melody and rhythm.

Sung this way, "Say, brothers, will you meet us (3x), On Canaan's happy shore" fits the (simple and presumably, original) melody just fine--no extra phrase is needed.

In "John Brown's body", the verse has the same basic melody as "Say, brothers" but a dotted rhythms are added in a few spots to fit in a few more syllables per line.

In "Battle Hymn of the Republic" quite a LOT more syllables are added per line, and a LOT more dotted rhythms added to make those syllables fit. The result is a rhythmic variant of the same basic melody as "Say, brothers" and "John Brown" (and the chorus of "Battle Hymn").

As to the longer version:


"Say brothers will you meet us on Canaan's happy shore,
Say brothers will you meet us on Canaan's happy shore,
When the day of Judgement comes?
Glory, glory hallelujah,etc."

This longer version is almost certainly a back-adaption of the words to fit the more rhythmically active version of the melody that was created over time through the John Brown song & variants and, particularly, the Battle Hymn. The Battle Hymn wasn't the latest of the variants in date, but it was certainly the most popular and had about the most syllables per line, and thus extra rhythms added, of any variant.

More, including scans from a historical hymnal showing how the "Say, brothers" text fits with the tune:

http://brenthugh.com/piano/john-brown2.html
http://brenthugh.com/piano/john-brown.html
http://en.wikipedia.org/wiki/John_Brown's_Body