Sorry to hear you're struggling. I do think you're very wise to seek help to make it through this rough patch. It's stressful, I'm sure.
Since LPR symptoms and allergy are very similar, my asthma doc did send me to a highly acclaimed ENT to check out my larnyx a year ago last Fall. I continued/continue to have some hoarseness, and my allergist suspected it was caused by continued reflux. He seemed to think the ENT would be able to decide if my larnyx was affected by reflux or not. The ENT did not think it looked like reflux, but rather a result of allergic coughing. However, since I was under the care of an allergist, he referred me to "the surgeon who does all the Nissens" for a work-up.
I had the testing, and the surgeon said that everything was intact and working just fine.
My PCP said that he would never recommend any other surgeon than the one I'd seen, and that if I thought I needed another opinion I should go to a center (Cleveland Clinic, etc.)
Anyway, I really didn't think I was refluxing (when I had my PH test pre-op, I was suffering greatly from refluxing when I was off PPIs...when I had it done post-op, I had no reflux, and was very comfortable.) Plus, although I still have enough allergic (presumably) coughing to cause hoarseness, my lungs are 99% better. I could say 100% but I suppose that's unrealistic, since I do have allergic asthma at times.
As Bill said, it looks like you would benefit from trying to get a second and third opinion, to see if you can find someone willing to redo a wrap for you, that appears "intact". When Bill had his second redo, the surgeon couldn't really figure out what was wrong until he got into the surgery an discovered it had been done incorrectly.
If you're having bile reflux, it certainly makes sense to try to get a tighter wrap, since it's the only thing you can do to stop it. I'm confident that there's someone out there who can help you. If you can get a tighter wrap, you might trade off some other symptoms, though...more bloating, tighter swallowing issues, etc. But if you can get relief from your LPR symptoms, it would be worth it.
As far as I know, the only way to keep reflux out of your throat is to keep it in your stomach with a Nissen.
Wish I could offer more information and help!
We're with you, Joe.
Hang in there.