Thanks for this write up!
You might already be aware of these, but I think there are some strong objections to the doomsday argument that you didn’t touch on in your post.
One is the Adam & Eve paradox, which seems to follow from the same logic as the Doomsday argument, but also seems completely absurd.
Another is reference class dependence. You say it is reasonable for me to conclude I am in the middle of ‘humanity’, but what is humanity? Why should I consider myself a sample from all homo sapiens, and not say, apes, or mammals? or earth-originating life? What even is a ‘human’?
I ‘disagreed’ with this, because I don’t think you drew enough of a distinction between purchasing animals raised on factory farms, and purchasing meat in general.
While there might be an argument that the occasional cheeseburger isn’t that “big of a deal”, I think purchasing a single chicken raised on a factory farm is quite a big deal. And if you do that occasionally, stopping doing that will probably be pretty high up on the list of effective actions you can take, in terms of impact to effort ratio.