Is it more "humane" for an animal to be eaten alive by another predator? The only difference is mankind has industrialized the process, and we don't truly give thanks because we are so separated from the process.
Edit: I don't really want to dissuade against alternatives, the problem I see is many nutritionally inferior options.
And re "nutritionally inferior", every dietetics and nutrition peak body on the planet agrees that a fully vegan diet is suitable for all people throughout all stages of life. In fact, billions of people have already lived perfectly normal, perfectly healthy vegan and vegetarian lives throughout history. If your diet — any diet — is nutritionally incomplete it's because you made the wrong choices.
1. We're talking about dairy. To my knowledge, humans are the only animal that harvest another animal's milk. An outlier in the animal kingdom. (i.e. not the naturalistic "circle of life" any more than plastic bottles or sarin gas.)
2. No, it would not be "humane" (as in "human") to eat something alive, but animals do it! There's a distinction there between human and animal, like squares and rectangles. I am encouraging you to lean into that distinction and be as humane/human as possible.
3. How far off of ideal nutrition would you be willing to go to save a dog? Would you give up broccoli if it meant no more dogs would be abused? Could you find a way to replace broccoli, difficult as it may be?