Not Too Late for Some Redemption (смешанная)

Students flood King's Cross Station to board the Hogwarts Express to school on 1 September like every other year since 990 AD. It is an expected and anticipated moment in wizarding Britain, just as the boost in sales across all retail places, but especially those on Diagon Alley, spikes hugely every August. This year, however, something has changed, and several students approached the barrier between Platforms 9 and 10 to begin the 1975-76 school year, only to arrive on the platform twenty years in the future.
How will they manage to find a place for themselves in a world in which they are already adults, perhaps working somewhere, perhaps already dead, their passing long since mourned? And how will the world they've entered welcome a group of Doppelgängers and ghosts?
Here is a playlist for the fic, and you'll likely see a lot of similarities between the songs in it and the referenced material in the work.