"People forget that the modern Scottish border is relatively recent - the Kingdom of Northumbria was made up of the North-East of what is now England and the South-East of what is now Scotland."

Only if you regard 1000 years as relatively recent! The border on the middle to eastern half of the country, the changing of Berwick aside, is basically as it has been since the 11thC. There were periods of Scottish or English occupation of one or the other but it was occupation never the less. Saying that your point is absolutely correct. There was a language continuum between the southern dialect of Scots and Northumbrian dialect of English because they were basically both newer forms of the old Northumbrian dialect spoken from the Humber up to the Firth of Forth.