The abandoned portion of the Hartsville site can be reached on foot from adjacent land that appears to be unrestricted. The two complexes are well-removed from separately bounded zones that surround TVA's equipment repository and the business park that now occupies a large chunk of the project's former land parcel. Apparently folks have been known to camp out beneath the tower, and there is a permitted deer hunt in the fall.
Because of the condition of the unfinished buildings, I have my doubts that formal permission from TVA could ever be forthcoming, so TheHiggs may have a long wait for the tour. Given the many unprotected fall hazards, I would not recommend attempting to access the abandoned building sites. However, if all someone wanted is that view of the exposed vessel, I think it is reasonably straightforward during business hours to drive up adjacent to the "A" complex via the business park and see the vessel and the tower up close.
I will be working to secure permission to visit and photograph the Satsop WPPSS site in WA, as well as abandoned infrastructure on sites in the Great Lakes-Midwest where projects were converted to thermal. If anyone can suggest a good first point of contact at Duke-Zimmer or at Midland Cogen (or for that matter who to talk with at TVA about visiting Bellefonte, where I understand that they did do a media tour recently), I would appreciate your input.