I live in Tennessee which last account I had was considered South. My family & several neighbors around always made Sauerkraut. I do not know how widespread the practise was, can only speak of those with whom I am familiar.
most of the "Churn Dashers" I have seen were simple crossed boards on the bottom of the "Stick" These were normally lap jointed in the middle so the two boards were flush. Have seen a few which were a disc with holes in it. Have seen pictures of some a bit fancier but these were the most common. I have my Grandmothers old Cedar Churn, but the bottom is out of it.
In making butter the object was to Agitate the cream, not tamp it down.
As to Cypress I am only really familiar with the Knees. I would have considered this too light in weight for an efficient Maul. I am however not familiar with the wood from the tree itself. We don't have Cypress in my area.
When we made a maul as I recall we generally used Hickory.