I'll guess "The Gamesters of Triskelion".
I can make some of the clues fit, but mostly I pick it because it is one of the episodes I have not eliminated based on clues and previous guesses.
1. Not sure about this, but three brains finally show up at the end.
2. Spock, crew and Enterprise finally catch up at the end.
3. Didn't have time to check the trailer, but it might be true.
4. One of the Thralls does not speak.
5. Not sure about the music and I didn't want to go back and listen to the whole score.
6. The only deaths are a couple of Thralls