Just called Stonehedge and talked with them directly. The noon til dawn refers more to the gift shop, and someone being there. Due to a conflict, there will be no one there tomorrow, and the building will not be open. However, the garden remains open for walking around, and it IS open from dawn until dusk.
So, anyone pick a meeting time? It doesn't seem to matter re the place itself. For myself, I'd prefer the morning
The girl also mentioned that they are having a big open free event there on Saturday and Sunday, May 1-2.