Hi,
Same thing happened to me. Pints of saliva produced at night, to the point of vomiting, so the vomit bucket was near the bed, This went on for a year. I stopped chewing gum- this helped some. I took prilosec 40 mg otc and this also helped diminished the saliva, then over time decreased to 20 mg. I also avoid spicy and alcohol- bc alcohol is bad for us. ( cancer etc)
And finally, when western medicine fails me, I look to acupuncture and voila ! No more hypersalivation. It's been 14 months without hypersalivation. I went to all the same MDs you did. There's "nothing wrong with me." And I had an EGD done and a colonoscopy. Pretty as a picture !