I usually open the pony, take the tail off, the put the head back in place. Protect the hair as you have done. The with a chopstick, I insert it in the tail hole and use it as a handle to turn the pony around.
Using the hair is another option, but it doesn't give you so much freedom of movement.
If you still don't want to remove the head, try inserting the chopstick in the tail hole pushing the tail a bit to a side.
I hope this helps!