I've done join up with almost all of my horses. As I'm sure you know, turning her back/butt to you is "disrespectful" and she's probably trying to show you she's the alpha (or at least that's my take on it). And from what you've said about how she is with the herd, out there she is the alpha. It seems from how you're explaining that she sits at one side of the pen and you go over to get her going again, which she then goes halfway around the pen and sits over there. Is that correct? If that's what she's doing, you should try staying more in the middle of the pen. I'd use my lunge line (not attached) to fling at her hind to move her forward (and not the clip end). Use a cotton lunge line and desensitize her to it first, by throwing it all over her legs, butt, back, etc. (all in a safe manner). Don't be afraid to increase your energy by being big and animated with swinging the line around in your hand or flinging it at her hindquarters. Remember, the whole idea of join-up is to emulate the alpha horse in the herd and drive your mare out, only then will she see you as the alpha. I'm sure you've seen her chase off one of the horses that are low on the pecking order, look at how she treats that horse, and copycat that energy and persistence.
You did say she was licking and chewing (and I'm going to assume inner ear was fixed on you, as this usually happened first for me), so you're obviously doing something right and making progress, but maybe once you see that you subconsciously relax a little or something, since you know you're also at the end. I had a mare that after inner ear and licking/chewing would want to slow to a trot and could trot for hours like that, so I learned to keep her at a canter to really push her out and make her uncomfortable out there. It took that same mare a few sessions to fully join up (and follow up) with me, but it eventually did happen.
I hope that helped in the smallest way, and best of luck to you and your mare!