Looking at the speculation above, how much of the imagery in these songs is the result of a combination of fanciful historical indoctrination of children by their homesick immigrant parents and the teaching of unrelated singing games by the teachers in the new homestead lands?

In the period 1850-1900, myriad poems extolling the deeds of old forbears were written and printed in American and Canadian books, magazines, and newspapers. Scots and English were prone to infect their children, and show their superiority to others in their new home, with poetry and songs, newly composed or paraphrased.
Old book stores always have volumes like this one, "Selections from Scottish Canadian Poets, being a Collection of the Best Poetry written by Scotsmen and their Descendants in the Dominion of Canada," pub. in Toronto, 1900. Of course it is some of the worst poetry ever published, but the books sold in good numbers.
A few quotes:

"Forward! see Scotland's gallant sons
Dash on to meet the foe,
Their strong right hand grasps Freedom's sword
And Freedom guides the blow;
Their bows are bent, their swords are keen," etc. etc.

"Then let us cheer his honoured name,
Sae dear to Scotland and to fame,
And on our feet, wi' loud acclaim,
Cry, "Hip, hurrah for Robin!"

"Then sing us to-night from the old Scottish songs-
The songs which our mothers would hear
In the old cottage homes, that were covered with thatch,
In a land that will ever be dear."

"Tonight we lift the minstrel harp,
With tears of sorrow wet,
And strike with reverent hand its chords
To wailings of regret;" etc.

"To chase in flight, by Carron winding slender,
The mail-clad legions of imperial Rome."

"Though haughty Edward looked in scorn
Upon the field of Bannockburn,
In terror thence he fled forlorn,
A long time ago."

Taking their parents stories based on fading memories of their homeland, made vivid through new books and papers like this one (which were also published for young people), children in schools of homestead settlements might entwine stories of ancient deeds and the singing games of the teachers into new ones that speak of olden times, but belong to a folk literature not from the 'old country' but newly born in the the new land.

Should we interpret these songs as survivals, or products of their time (1850-1900)? Just something I have wondered about but I don't think that there is a clear answer.