@Monochromatic Rainbow 300 in old miles, new miles, Welsh miles, Irish miles, Scots miles, Dutch miles, Austrian miles, Prussian miles, or Hungarian miles?
Point is, the definition of "mile" cannot be assumed to be equal to the statute mile used by the British Empire, especially for a setting most closely imitating the 1400s in setting equivalency.
If we go by the oldest definition of a mile, that being 1000 steps, and we approximate one guy's pace as 1 statute yard, then the mile is now defined as a whopping . . . 3000 feet. Nearly half of the statute mile. Then, we take your former assumption that half of the North is uninhabited save a few ME STRONKs, that brings the population density up to a generous . . . 3.2 guys/square mile.
Yeah, I suppose you're right, and that does sound a bit unrealistic. Mathematics, amirite?