I think one important bit of info is that there is A LOT of metal out there. I thought your Meshuggah example was a good way to say what you were thinking. Luckily for you, you aren't the only one out there with this feeling.
I personally love the death growls and screaming. I think that's part of the attitude. But the key is that you're looking into bands like Opeth and Meshuggah. That's part of who they are and it's part of what makes them work. Now I have 2 suggestions for you if you're looking for some quality metal that won't make your ears bleed.
1. Find some melodic death metal. These are bands where the music is heavy and the vocals are growly, but where they really add to the experience. Bands like In Flames, Children of Bodom, Amon Amarth, and even Dethklok use the growly vocals to build the music. All of the sounds combine together to make a great sound.
2. Expand your horizons. There's a band for everyone. One I think you'd be interested in would be Pelican. Same heavy metal aggression with prog rock feels, similar to Mogwai. And no vocals. Very good band. Some others you could check out are God Is an Astronaut, Russian Circles, and Explosions in the Sky. Also look into some prog metal bands who effectively use singers, like Mastodon, Tool, Porcupine Tree, King's X, and Death. You may find some stuff you like.