My best guess at the Real vs Imagined progress

Honestly, they've made good progress on day 3, similar progress to what they imagine they've made which couldn't be said for day 2 where they thought they had made it like 10x the distance they actually did.

Only real hang-up is Lud thinking that Shikoku (the island in the middle of the image) is called Miyazaki or at least that Miyazaki city is on Shikoku. Only way I could get that to line up is making Kyushu way smaller and Shikoku way longer.