1. [any of the 'plausible' scenarios where Rome takes over most of the world]
2. Rome begins collapsing catastrophically in the 1800s
3. Canada and Ukraine are, at this time, the only two regions of the world that adhere to a strict branch of a certain religion
4. After establishing themselves in their own right as states in the 19th century, a plebiscite in 1920s Ukraine votes to merge as part of an Empire with Canada
5. Theocratic, post-Roman, Canadian (though full of Roman settlers' descendants)-Ukrainian (full of descendants of Slav-Roman children) Empire declared under Augustus Canadus.
I can't see any fault in the above logic.