There is a fortunate coincidence here. There are wealthy vegetarian castes in India, and India tracks demographics by caste, so it's likely that the data is out there for us to figure this part out.

An alternative is to do something like follow second-generation Western people of Indian origin. I know at least one study of Tuberculosis in the UK tested the effect of vegetarianism there and used the British Asian sub-population to do so, so there's probably some info there too.

I don't know of any other large vegetarian groups.

Well at 133rd there are plenty of 3rd world countries above them. There's only 185 countries on the planet. It certainly shows that meat consumption doesn't hurt.