Hi Aunt Kay. My thought is that your wrap is probably okay, but your motility problem is worse. I didn't even know I had a motility problem until the Nissen and didn't have any problems until afterwards.
It was described to me this way: Because my LES was so weak, gravity was the driving force for swallowing for me; post nissen increased the amount of pressure..creating a "normal" negative pressure that is normally counteracted by the force of the contractions of the peristalsis of the esophagus when swallowing. In motility problems, the muscles contractions are not strong enough to counteract that negative pressure, thereby causing swallowing problems.
So, in my mind, because you're having increased problems swallowing, it sounds like your LES is still producing adequate negative pressure against the esophageal contractions..it's the contractions that aren't able to counteract that pressure.
Have you and your GI explored the motility issue any further?; that may be your next step.