Start by writing a biography for him. You have a list of sources, but what do those sources tell you about his life?
He was born about 1844. Do you have an idea of where he probably was born? It's not likely that there are government records of adoptions from that time period, but if his birthplace was a small town, you might find some clues in church records...
If there are male descendants on his "Smith" line, Y-DNA tests for those relatives might help in your quest. And if you develop a reasonably complete family tree for yourself, autosomal DNA testing for you and siblings and cousins possibly might lead you to some matches who aren't on any of your [other] known lines.
