Very primitive -- sort of Outsider Art, I suppose. How do you find out who carved a stone, especially a one-off like this one?

Usually through what published researchers before me have confirmed. Other times it's an educated guess on my part based on what I know of their style.
In this case it was the former, but even without the citation I may have figured it out on my own because the way any stonecarver does lettering never changes, no matter the icon. And John New had a certain way of lettering I recognize.

Thank you for the education! I'll keep my eyes open for similarities and differences in the future.

Living in Eastern Connecticut, there are many (even dozens) of older graveyards in the area. I'll have to start learning who did what. My town sexton might be able to help; the last one didn't give a d@rn.