The problem with including North Africa (not counting Egypt) is that it basically was Europe in 600 AD. Just have Mauretania or a united North African empire based in Carthage repel the Arabs and establish independence from Byzantium, and they can follow the path of Iberia very easily. In addition to North America itself (serving as the United States equivalent, spreading across the continent with huge population, resources, and cultural output), they could have South Africa or Brazil as that. Or all three even.
Mauretania might be best as the most "non-European" since it could end up speaking a Berber language with a 600 AD POD. Considering the sea routes and their potential goals (at some point they could want to bypass the trans-Saharan trade by going a coastal route), it isn't impossible for Mauretania to grab Brazil, South Africa (which has a lot of coal for industrialisation of coal-poor Mauretania proper), and Australia, and possibly much more, creating a bunch of Berber-speaking settler colonies (although Brazil and South Africa will be mixed-race societies, but could get a lot of immigration as well). So here it's very possible to have 600-1 billion people speaking a Berber language natively with Berber as required to learn as English is (or at worst, as important as Spanish globally).