To clarify, I'm not saying that "Scotland the Brave" comes from "The Irishman's Toast." The opposite is far more likely.
References to the Scottish march suggest that it became popular around 1880 and was circulating anonymously among Highland regimental bands.
Surprisingly, "The Irishman's Toast" looks to be the earliest printing of (a clearly recognizable variant of) "Scotland the Brave." It seems impossible to know for certain when the modern version became current, because printings are so surprisingly late!
It is just possible that Hyslop's poem either inspired the tune, or (less likely) was inspired by it. It's surely significant that the poem's unusual scansion almost perfectly matches the tune, and that it ends with the words "Scotland the brave!"
The 1934-36 confusion of "Scotland the Brave" and "O'Donnell Aboo" is to me also surprising. Maybe it was simply someone's misrecollection or misunderstanding that became enshrined in print.