We lived in an Elizabethan Cottage for several years which had a cellar. Although it never flooded it was always damp. A builder suggested digging down from outside wall then knocking bricks through from inside to exterior excavation. Down piping, a couple of right angle unions and grills completed a venting system. The inner grill was about 5 feet up from the cellar floor and you could feel through your eyes a constant flow of air coming in from outside. Cellar was noticeably drier afterwards.
Not sure if similar would be possible for your pit but it could be aided by a small computer fan if needed.
