I have to say, I find Everlane's tees a little flimsy and don't buy them anymore. I do like the fit of their box cut tee, but still too thin for my preferences and the stitching started to unravel after just a few washes.
My favorite tees are the Uniqlo U crewnecks. They are a classic, more fitted style in a substantial 100% cotton. One of the few tees I've found that isn't too long. I don't like to tuck, so tees that hit at low-hip are pretty useless to me. They only come in crewneck, but I think the regular Uniqlo Supima tees come in a v-neck.
You might want to have a look at Entireworld or Richer Poorer. I haven't tried either of them but they look like good candidates. Not sure if they do a v-neck though.