I've thought of two different answers which fit most of the clues, but they both fail to match up at one point.

Regaining Cloud's memories is an obvious one (kind of surprised no-one has mentioned it already, to be honest), with the only line I can't see fitting it being "Midgar is the solution, it seems". Unless somehow that refers to it being the final step on his journey before Tifa finds him? As I said, that one doesn't quite fit, but everything else works well.

The other is the Turtle's Paradise poster collection. Minor task, with an easily missed aspect in Midgar that requires you to take a journey all the way back way later in the game. I can't see it requiring help from the "absentee", though, unless it's somehow referring to you finishing the mini-quest in Wutai, and the possibility of Yuffie being out of the party when you do.