I think that you should consider that he changed his name. When you can't find anything, anywhere, on someone, that's a name change. He's not in the WWI draft reg, I can't find him on any censes. Usually when there's a name change, it was because something bad happened- like criminal activity, although sometimes it happens when there was a divorce and the mother remarried, the child took the stepfather's name.
I would try to contact the courthouse where they were married and see if there is a marriage license application. A lot of places have those, and it lists parents and birthplaces. You need to contact the Probate Court of Mobile County. http://probate.mobilecountyal.gov/
Does your mother recall anything about aunts, uncles, etc of Walter, anyone coming to visit, any stories?