When does *The Miracle of Endymion* occur?
When Index asks Touma what Endymion is, he mentions it's been visible before, including when she holds a grocery bag while standing next to him. This flashback is to footage from the end of the first II opening. This doesn't contradict the above placement of Miracle, although it does require said footage to occur early in (or before) II.
In particular, the aforementioned flashbacks are doctored; for example, the II opening doesn't include Endymion.

This is supposed to be a tongue-in-cheek gag. Index is breaking the 4th wall a bit by pointing out how strange it is this space elevator was never pointed out before despite being under construction all this time in the background (because in real life it hadn't been conceived of yet so obviously it wouldn't be in the story back then), and Touma casually retcons it into existence with a few flashbacks where it's been inserted into a few scenes.
This is a way of acknowledging the awkwardness with which its inserted into the canon and timeline of the series and allowing the story of the movie to progress onward without further attention paid to it.
So, in answer to your original question, the timing is as you've sleuthed it out to be. It's meant to take place between the tree diagram arc and the festival arc, and they playfully retconned some scenes to make it fit into the timeline despite a lack of evidence for its prior existence. The commentary tracks on the movie also confirm this is the case.