Remember, Stress, which the adrenal glands are in control of, inhibits gastric acid secretion.
Rebuilding the adrenals is key to shutting off this mechanism. I personally don't know of the true efficacy of salivary cortisol level testing (4x/day) but I got my results back a month ago and well, I'm a walking dead man! I have a strong reason to believe that the adrenals, in some part play a role in acid secretion.
Here's a quick abstract to check out. Read the last sentence.