I realize we're just being silly here, but I think it's important to point out that it's kind of a misconception that deforestation is caused by logging. It does happen, but not as often as other causes, primarily clearing land for agricultural uses. Source
It also says in that article that if everyone ate a vegetarian diet we could reduce agricultural land use to 1/3 of current usage which would have a much bigger impact than stopping logging.
Of course, it's better not to waste the lumber since the trees are being cut down anyway. My point isn't that logging is good, but that there's a much bigger threat in regards to deforestation that has an attainable individual goal where we don't need to rely on greedy corporations changing their minds. There are admittedly a huge portion of people who will outright refuse to go vegetarian but any vegetarian people will make a difference. If 50% of people go vegetarian that means we'll use 1/3 less land. 25% of people means 1/6 less land, etc.
Addressing climate change requires a multi-pronged approach and every little bit helps.