Metal Vs. Classical

Your professor sounds like one whom is too hopelessly absorbed by his own convictions and his own obstinate "I-must-always-be-right" mentality to be pleased with your selection.

Still, since you're seeking something without any orchestration, I would suggest something from Dream Theater, perhaps either the "A Mind Beside Itself" trilogy or "A Change of Seasons," that is, if he's actually willing to listen to such lengthy pieces. I say this because the vocals are clean and somewhat-operatic, and the music is very guitar and drum-oriented, generally melodic while still retaining that seminal element of "powerful heavyness" that I feel defines the metal genre. Nightwish initially seems like a befitting choice, but I suspect that the epic classical-influences are far too prominent in their repertoire for him to awknowledge it as something original and devoid of an obtrusive classical-inspiration. Nonetheless, I sincerely hope he accepts your piece and it works out fine, since his judgment apears to me like a very unfair and opinionated one. Shouldn't professors be a bit more pragmatic when it comes to their evaluations?
 
The Chasm!!! Anything from Deathcult for Eternity - The triumph is brilliant. I would probably recomend the 4:th track on the CD, or the 7:th or 8:th. The vocals shouldn't bother him as much either since they are not very obtrusive in the music.
 
Compared to Beethoven, you're screwed (Beethoven would have understood the underground metal ideology also ;).

See if you can get the guy to let you compare it to other mediocre mainstream composers like Copland, Mahler or Schoenberg. Then play him Burzum, Emperor, Demilich or Morbid Angel.

Opeth is a joke.
 
Whatever you play him, you can guarantee that he'll dismiss it as being crap, or at least certainly not up to a 'Beethoven standard'.

But for what it's worth, i'd try Dream Theater.