There's absolutely no way they hiked the trail up mount Inari at Fushimi Inari-taisha with those time constraints, which is a shame as that was the best part of seeing it when I visited.
The route begins at the Inari shrine, so it's not too bad. Going down is much faster.
Thanks for adding the itinerary, it looks fun. I might do it in two days without the last points if I go to Kyoto one day.
Aaaaaand as it turns out, I made a huge error with the route. One that I really should've noticed.
Without going into too much detail, the author typoed when writing it on Kaoru's paper. They used the wrong kanji (characters) to write the name of a temple, and it just so happens there's a temple that's kinda similarly named to how she typoed it, also in Kyoto.
That's what led to that maaaaassive trek over towards the west of Kyoto. That was a mistake. Oops! That trek was also practically impossible within the time constraints.
Now everything is much tighter together and (almost) reasonable to walk through in one day! The TL notes page has been edited with the new route and the correct temple.