How do you know the identity of who carved this headstone over 300 years ago?

Sometimes what's been written on the subject. Other times I base it on photos of other stones whose carvers were positively identified.
The latter was the case here. I'm fairly positive it was Hempstead's because this was his style. ^^

Have you ever considered publishing a book on this subject? You seem to be extraordinarily knowledgeable. Seriously, 18th century New England funerary art is a niche subject, but it's one that you'll probably find interest in.

If you like I could potentially help edit for a share of whatever you make on it. I've got some experience writing history articles (I actually published one on Encyclopedia Britannica's website) and I have some background in art history, so if you have some trouble getting the info into a coherent form I can help.

I'm kind of backlogged at the moment but I'd jump at the chance to do this.