Is the chimney open at night? I think that would be a cool place to get a night sky shot up a tube. A shot in the early evening with enough light to see the bricks like your shot showed, then a evening one with just the circle of stars and then the two combined, I think would make a nice picture, kind of like the straight up shots of the redwood trees people take in California.
Yeah, these areas are open at night, there's no lockable gates or anything. one just slips through a gap in the fence designed to keep kangaroos out. That wold be a cool shot for sure! I like those time release shots of the stars moving that photographers create on editing software too, that would look good!