747 performances, wow. Figuring from when the Met opened in 1883 up to 1972, that averages out to a little over 8 performances every season. I saw only one of those 747 performances (Nicolai Gedda and Jerome Hines).
I'd read about The Nose earlier, and I couldn't figure out from the skimpy plot descriptions exactly what it was satirizing. But "councillor" and "church" answers that question. Since it's Shostakovich, I should have known it would be political satire. Since you say the music isn't particularly memorable, that throws more weight on the story. Frankly, the story sounds unpleasant...starting with the barber's discovery of someone's nose in his beard.
Austin, there's been one repeat so far -- Lucia. But they were different productions as well as different casts.