OMG this is the funniest, sweetest, most satisfying story ever!
I've been sitting here drinking tea and laughing out loud. The "Eileen Prince - Im a Prince - Irma Pince" theory I've only heard once before, and you use it here to great effect. The Eileen-Argus romance feels like an extra bonus track, and your handling of those flinty lovers, Snape and McGonegall, is spot on and skillful.
This is heartwarming:" 'I see," said Minerva. She moved a little closer, and started reading. "I shall remember this the next time I feel like a dungeon holiday.' She rubbed the back of his neck until he looked up and gave her an awkward, crooked little smile." Is the kind of sweetness that made me wish I was Minerva. Without undue hinkiness, you managed to keep reminding me that Severus is only 28 here, and an immature, needy 28 at that.
It's usages like this - "Argus, nearing the unfamiliar territory of a witch's bedchamber, made up his mind to give her the best seeing-to that he possibly could." - that in one sentence convey background and character as well as provoke a laugh with an unexpected usage - that make this story so rich.
Really well done, Mystery Writer. This was the treat of my day.