Well, I showed a friend (who listens to Star in LA on the Radio and finds most metal with death vox makes him feel "dirty") Bleak, then Demon of the Fall, then In My Time of Need, etc. He really liked the vox, and thought they "aren't goofy, just interesting". So there's always hope.
So I would say Bleak over the Drapery Falls (as the end of DF goes on for a while and there is more musical progression in Bleak) if you want something from BWP.
Probably a better idea is to go with something from Still Life (The Moor, Godhead's Lament, Moonlapse Vertigo) and Give Them the Lyrics, explain the concept of the album, and what stage this is. If you wanted to go farther, show the different musical styles. Talk about the folk in Godhead's Lament, or, what I love, the very "musical-esque" section of The Moor, the "Melinda is the reason why I've come" section. Straight out of a stage musical in delivery and composition. Don't just hit play. Explain how things are structured, what the story is, etc.
Similarly, if you really, really, really were hell bent on playing Demon of the Fall
then again explain the concept of the album and the actions that take place in the song. Explain the use of the demon vox thematically and compositionally, drawing parallels between the very oppressive and sad layers of guitars with the same textured layering of the death vox in the beginning, eventually thinning to a lone death voice, then finally, as the inital anger has run its course, in a more reflective state the clean vocals come in with "Run away, just one second and I was left with nothing" and talk of how that situation would be for someone, that entire loss, the realization of being an apparition, and having lost your love. The line "Her fragrance still pulsating through damp air" says so much, it demonstrates his feelings, his yearning, and reaffirms that she to him is now simply a scent on the air, a phantom, as he is through death to her. And then "that day came to an end". Well have a discussion on what "that day" is/represents. Their love? His hope? Many things could have ended then. Also, if you wanted to draw a parallel, you could (gulp)
show some of the scenes between Bruce Willis and his wife in the Sixth Sense when he sees her at the table on their anniversary, and when she starts to like that other guy. I'm not trying to cheapen Opeth in any way; I think that thinking about Opeth is the first step to liking them, and this will be a good thing in class b/c they will be able to relate to the movie and their own experiences, and then really look into the lyrics, and then the music, etc.
Man, I should get back to work. Stupid Opeth and their plethora of fancy candies.