"Could we set up a sentence like 'Burkina's armed forces is leading the country over..'"
I think you misunderstand the function of "over" in the original sentence.
Ben is correct. However, here is further explanation of the background of how "over" is used in the original example, to broaden your understanding of the many uses of "over".
"Over" can be used as a preposition (as it is in the original example - you can check at oxforddictionaries.com) that is often associated with the following similar verbs (and their nouns) such as: argue, quarrel, disagree, debate, feud, battle, fight, struggle etc.
EXAMPLES:
They argued over who would lead the country.
The argument was over who would lead the country.
They fought over the rights to the gold mine.
They had a fight over over the rights to the gold mine.
So I said that you misunderstand the function of "over" in the original sentence, because in the original example, "over" is used because of "split", not because of, or associated with, "leading". I hope you now understand more about this way that "over" is used.
