This is a long shot, but I would imagine you're open to any ideas. When I had my lap band, sometimes when I ate too much, I would get radiated pain into my left shoulder. Occasionally, it would happen even if I wasn't eating. It turns out that in the case of the lap band, sometimes it would rub against the vagas nerve, and cause those pains.
Now I realize you don't have the band, and so far, since I had the band revision to bypass, I have not felt the pain, but maybe there is a possibility that when you are drinking, something is hitting the vagas (or some other) nerve. I don't think that is something that is going to show up on conventional imaging, but maybe an MRI?
Again, just a thought. If you search for vagas nerve, you will see it is somewhat common with the lap banders.