Hmm, I'll have to think about this for a bit. But the first thing that comes to mind is to start out walking her in a large circle, and slowly make that circle smaller. I would use my right hand to try to keep her as straight as I could while I was walking those smaller circles. Try to get her to cross over by a small amount while walking. Maybe that will help get her unstuck. Don't expect much, though, at first. If I got one cross over step, I would immediately go back to a larger circle where she didn't have to cross over. Just small amounts at a time.
Also, can you pull her to you and make her cross over? Just thinking out loud here, but what if you had her set up, stepped away from her and into a spot on the expected track she/you would take, and then slowly take up the slack in the lead, and then give a hard pull to bring her towards you, hopefully getting her to move her front end over. Maybe doing this to the right and left.
Another thing - do you have a place to free lunge her at? If you do, I would get her going nicely to the left, and then make her rollback away from the center (into the rail) and come back out the other side. I'm thinking that if you can get her to stop and get away from your body while doing that, it might help some with the showmanship.
The only other advice is that I would not be afraid to get tough with her (to your ability, and not beating her, of course). It already sounds like you are, and it sounds like you are starting to get her attention some when you are slapping her with the rope. Maybe try a dressage whip, and as long as you can stay safe, get after her and the second you get her to move ONE step away from your body with her front end, even if her back end also moves, or she doesn't really cross over, just moves away, reward her like crazy (lower the whip, walk up to her and talk, rub all over her, and just let her know she was a good girl).
To me, it sounds like she isn't respecting your personal space. If she stepped on your foot, would you be able to move her off of it?
Sorry for the rambling. Maybe you can get an idea from here.