Upvote:5
I doubt you're going to find an "official" listing anywhere. Reading between the lines of the article, it sounds very much like this is still an active cemetery, meaning that there's points where it's open.
During my visit, I counted at least half a dozen signs warning visitors that trespassers would be prosecuted, even though the front gate was wide open and fresh flowers were propped up against shiny new graves.
So the gates were open on the day Matthews visited, but not 6 weeks later when Craig did. My bet is that the cemetery is open when it's open (i.e. someone comes to open it up, which doesn't happen on a regular basis). Most of the comments about it on Roadtrippers point to it being closed most of the time.
If the gates are open, you should be able go in. I would expect any passing law enforcement to stop you and at least find out what you're doing there (and neighbors apparently actively report people in the graveyard). They may also ask you to leave. It's unlikely you would be arrested for merely looking around if the gates are open.
Is there a specific process for obtaining a permit or otherwise requesting permission from the cemetery owners that has a reasonable chance of success
It doesn't seem so. The owners of the cemetery wish people would just forget about it. Hence why the TV show Supernatural made their own Stull Graveyard somewhere else.