I've been in a few houses that had open wells right inside them. But the description of the site in your post reminded me of an Archaeology class I took a couple years back and we discuss a building technique used in the south called "Earthfast" or "Post in Ground". Might explain the shallow cellar hole and absence of stone. I dug out one of my books "In Small Things Forgotten" (Deetz) and this is a part of his description:
"An entire building tradition in the seventeenth-century Chesapeake has vanished leaving hardly a trace; only two examples have survived the passage of time. Known as earthfast or post-in-ground construction, this tradition involved framing the house on posts buried directly in the earth. What has survived of houses of this type is little more than a faint pattern of soil stains, marking the location of the posts, to be seen only when the plowed earth has been removed, and then with difficulty. This building tradition was linked to a number of economic factors, to be discussed later, and was the commonest form of construction throughout the seventeenth century and in some places into the eighteenth...."
