Going back to Scotland for a moment, another useful source on the English/Scots/Gaelic question is R.R. Davies' "The First English Empire: Power and Identities in the British Isles 1093-1343" . His answer to the question also involves English emigration to Scotland during that period, but he stresses the agricultural-technology side of the issue rather than the military. The English had mastered a more productive set of agricultural technologies by that time, and Scottish kings and nobles were happy to encourage its diffusion through emigration. It's also useful to see the issue in the context of the similar emigration of English agriculturalists into Wales and Ireland in the same period, which Davies covers.

This doesn't invalidate the military technology argument; I would imagine they are complementary. Medieval military technology required a lot of agricultural productivity to support it, after all.

Finally, it's hard to talk about the triumph of modern English over old Scots without mentioning the role of the Reformation and the Church of Scotland's decision to adopt a standard English Bible rather than commissioning a Scots translation. I suspect that was perhaps the deciding factor in the end.