Songwriting is Word Sculpture
It is hard to nail down what goes on in a poet's or a song writer's head as they sculpt words and phrases to craft a verse. (As a dabbler in poetry I reach far and wide for rhythm and rhyme. It's not as easy as it looks).
Any estimate is at best partly right without an explicit statement from the artist. But there are some clues.
Whence "Christ Was Born Across the Sea?"
A songwriter alive in the same time period penned a Christmas carol about the news of Christ's birth being "brought from oversea." The artistic point is strikingly similar to Howe's "Christ was born across the sea."
The Christmas carol, written by best estimates a few years before Julia Ward Howe wrote the Battle Hymn of the Republic, uses "oversea" which means "across the sea" quite literally.
The term "overseas" comes to English from the French outre-mer. The capitalized version Outremer was a general name given to the Crusader states established after the First Crusade: the County of Edessa, the Principality of Antioch, the County of Tripoli and especially the Kingdom of Jerusalem. It is in that land where Jesus was born: Outremer. (The Holy Land, more or less ~ oversea ~ across the sea).
Masters in the Hall is a carol crafted by William Morris sometime before 1860. The carol is a song of celebration of the promised birth of Christ the Lord.
Masters in this Hall,
Hear ye news to-day.
Brought from over sea,
And ever I you pray:
Chorus Nowell! Nowell! Nowell! Nowell, sing we clear ...
I know about this song because we sang it in sixth grade choir. It wasn't until I was an adult, and learned about Crusades/Outremer, that I made an association between the two.
It's a song that is contemporary to the Battle Hymn of the Republic. Did Howe borrow from that tune, or did she as an educated person have enough familiarity with history, the classics and poetic styles to arrive at the same turn of phrase independently? Unknown, and either answer is as likely. Her story is that she came up with it on her own ...
I went to bed that night as usual, and slept, according to my wont,
quite soundly. I awoke in the gray of the morning twilight; and as I
lay waiting for the dawn, the long lines of the desired poem began to
twine themselves in my mind. Having thought out all the stanzas, I
said to myself, 'I must get up and write these verses down, lest I
fall asleep again and forget them.' So, with a sudden effort, I sprang
out of bed, and found in the dimness an old stump of a pen which I
remembered to have used the day before. I scrawled the verses almost
without looking at the paper (Howe, Julia Ward. Reminiscences: 1819–1899. Houghton, Mifflin: New York, 1899. p. 275.)