First of all, I'd like to apologize for taking so long to get your post online and to respond to you. I've been working long hours, 7 days a week at my day job, so I haven't been able to pay as much attention to this site and my visitors as I would like.
But enough about my woes... Let's talk about yours.
I hate to take sides, but I'm inclined to agree with your Gastroenterologist. The most recent research indicates that bad breath does not originate in the stomach. Even when someone experiences situational bad breath caused by something they've eaten, i.e. onions, garlic, etc, it's caused by compounds in those foods interacting with Anaerobic bacteria that live in your mouth. There are a few exceptions to this due to medical conditions, but your hernia isn't one of them.
Now, something I do know is that the discharge from your sinuses is rich in proteins, and guess what. Proteins are the favorite food of Anaerobic bacteria. In fact, their job is to begin the break down of the proteins in the foods you eat. As a result, they produce waste in the form of compounds that don't smell so good, resulting in bad breath.
