Thinking more about it, it still seems to me like the roads are the main problem. I didn't really design any major roads that lead from major settlement to major settlement, just minor roads that go from village to village, some of which incidentally happen to link up towns and cities. That feels like an area where I should put in some more work. It'd make it feel more naturalistic (at least to me) to put in major roads linking major settlements, then have more of the small paths be offshoots from those, rather than all roads being roughly equivalent. That would reduce the feel that all the roads are on a strict grid.

It doesn't necessarily match the history of the island -- there has never been a major conquering technological power with a love of straight stone roads, unlike England had with the Romans -- but still, major settlements are likely to be connected by larger, more solidly built roads.