If you are at am impasse, have you actually located all the possible relatives who might be able to help you in your search?
My wife's great-grandfather "disappeared" ca. 1918. I'm not certain if he was in World War I or not, but I do know that it is possible that a descendant of one of his five siblings might have heard what happened to him. My wife's family does not know. However, it is possible that years after he left, he made some contact with a sibling and that information was not shared with this great-grandfather's children.
So my search for him is not complete until I have worked on locating the descendants of his siblings.