I think the answer is mostly two, with a little side of four. Nutrition science is very difficult to perform correctly, because of the difficulty and cost of randomized controlled trials of diets. In particular, the China study was not controlled, and it was performed via surveys (which have a reputation for being inaccurate in diet studies). Added to that is the fact that food isn't really about food. It's deeply intertwined with our sense of personal identity and culture, and that leaves you with many researchers stretching their relatively weak evidence a little bit further than is warranted. Once you get as far removed from the actual science as recommendations from the FDA or Harvard School of Public Health, there is virtually no room left for nuance, and they are already making recommendations from a public health perspective, which is not the perspective you seek.

With respect to confirmation bias, I suspect there is some of that going on. Specifically, you say, "There are lots of people who are PhDs of exercise, anthropology, or economics who criticize his recommendations, but I have a hard time finding a mass gathering of nutrition scientists coming out of the woodwork to shoot down his recommendations." There are probably not "mass gatherings of nutrition scientists" who disagree with the China Study, but there are mass gatherings of experts in medicine and various biological fields (and maybe the odd nutrition scientist) who would probably disagree with the China Study. Googling "paleo conference" I could easily find several such mass gatherings. So you aren't wrong, but you are implying more with your selection of outsider expertises than is warranted (exercise, anthropology or economics, rather than doctors, biologists, etc.).

With respect to the object-level consideration, I recommend you read Stephan Guyenet's recent series of articles on meat Is Meat Unhealthy?, which considers both positive and negative factors of eating meat. He is not a nutritional scientist (he is a neurobiologist), but he is by all appearances a careful scholar. You can read the summary first if you want to see his ultimate conclusions, which don't strongly support either the "vegan" or the carnivorous sides of the debate.

However, with respect to the China Study itself, he only touches on it in this series thusly:

The China Study

The China Study was a massive ecological study relating diet and lifestyle to chronic disease risk in China. It has been invoked by researcher and vegan diet advocate Colin Campbell to support the idea that animal foods promote cardiovascular disease and cancer, even in the small quantities that were typical of the regions studied. After having reviewed the study data, the publications based on it, and the various commentaries on it, it appears relatively clear that the China Study does not support the conclusion that meat consumption is associated with cardiovascular disease or cancer risk (17, 18, 19, 20, 21). Everyone seems to agree on that, except Campbell and certain other vegan diet advocates. I won't discuss the China Study further.

And elsewhere has criticized it on methodological grounds (e.g. here)