I read through your post, and I guess my issue is that I don't really know if 'settling' is exactly the correct term in european case, for although that is what did happen in effect, it was often probably incidental / secondary to another process. And by the that, I mean that is seems to me that there must have been something awry at home, for we, the descendants of the europeans, to actually go and settle all these lands at such a large scale. If you are a historian, you tell me why.
Did they need space for convicts, so that's the reason for making space in places australia and french guiana? Was there religious strife in europe, causing people to flee to america, and did some also come, conversely, to practice an even more austere version of their religion? Was there overpopulation? As to the slave trade, what is the origin of having such a disrespectful view of labor itself, to cause there to be such a mass market for slavery? And so you see, the 'settling' might have been incidental to many primary headings, making it more of a symptom of something else
I think maybe what happened, is that the europeans become 'unsettled,' and that is why I am flung out here in the american midwest, as opposed to being somewhere in britain. If you can't establish an honest economy, relation to religion, law, population level etc., then something isn't stable.