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I'd argue the most ethical course of action is to halt the breeding of additional animals for the purpose of slaughter. We have complete control of the situation here: not all wild animals die gruesome deaths, but a livestock animal's fate is decided far before they are even born. It feels a little less than 'humane'.
I agree that this is probably realistic but still incredibly difficult to call 'humane'.
Here's a definition from a quick web search:
Would you say that an individual who has the choice not to kill an animal and does it anyway is doing a 'humane' thing? Does it make difference where that killing happens?