Stance Widths
Braden,
My own stances are a pretty much the same as yours. My kou bu is about hip/shoulder width, and has 100% of my weight on one leg. Consequently, my Rhinoceros Looks at the Moon, and Close the Door and Push the Moon stances are single weighted as well. And my stances are much thinner than those in the book.
If you do Violet Swallow single weighted on the back leg, then your left foot should automatically turn with your body. In these particular postures, I can pick my left foot up off the ground without having to transfer any weight. Your left palm should strike your right arm at the moment your weight settles onto the right foot. From there you turn to your left and do the Rhinoceros posture.
Now, maybe I’m confusing you here, but this is the way I think of this turn. It’s not as tightly coiled as Close the Door and Push the Moon. Close the Door is really tight. Rhinoceros is a bit looser. (larger framed?) Anyway, while Close the Door has that little turn back the other way first, Rhinoceros does not. You turn straight to the left and open the arms.
I think the reason lies in the application. you see, with Close the Door, we are out at the edge of his wrist, or on the closed side at least. We can do our small circle lock, or our lower strikes because we have room to maneuver. But for Rhinoceros, we have a different use. We block a punch with the Violet Swallow movement, but he is very close. So we have to immediately turn and strike, without the leading movement on his arm and without the coiling beforehand. We strike to his chin or nose, turning his head upward (thus the name). And the lower hand strikes to the ribs.
Now, I think of Close the Door happening on the closed side of an attack, and Rhinoceros happening on the open side. (On the open side, we are in between his hands, in greater danger.)
If you are single-weighted on the back leg, and turn immediately to the left, then your left foot should turn outward naturally when your body turns. It should happen this way for Close the Door as well.
Remember that your gaze follows your left palm until it strikes your right arm. When you actually do Rhinoceros, you look straight forward along the circle, not at one of your hands. Your gaze returns to your right hand on the next strike.
When we do the directional changes walking the circle, the footwork is kind of the same as in this posture, when we do the inside turning change. If you are walking ccw, and have the right foot forward, then you turn both toes to face the other way and walk around that way. But the toes do not turn at the same time. The right toes turn first and then the left. (There is only a split second difference, but it helps you maintain your root.) Now, while doing Violet Swallow and Rhinoceros, you first kou bu to do Violet Swallow. This is the same as turning the right toes inward. (So I guess technically, we kou bu in the transition, doing kou bu before we turn the left toes out.) Then a split second later, we turn the left toes outward as we thrust the hands into Rhinoceros.
I, too, think being rear-weighted is important here. I think it’s a bit like shooting a rifle. You can hold the butt of the rifle in the air when you fire and it will recoil quite a bit in mid-air. But if you have the butt up against your shoulder, it will not move (unless your shoulder does, LOL). Being rear weighted here has that feel, like firing a rifle round. And being rear-weighted seems to add snap. Maybe that’s not a good analogy, I don’t know. But I’ll leave it in this post to see. 
If anything’s not clear, let me know. I’ll try to elucidate.
“To enter is to be born, to retreat is to die.”
-An Old Taijiquan Saying