We finally went to a university hospital where they did all the typical GERD related test and as soon as they discovered he actually had GERD, it seemed like they concentrated on that as being the source of his
cough, and stopped listening to what he was telling them, that the
cough would start as soon as he ate food. It didn't have enough time to get to his stomach and then start to regurge. But anyway, I finally stumbled across the answer in our local newspaper's doctors column.