Searching for Elijah's ancestors if of course what comes to mind first, but just a reminder is that it is a "Connect 1900" challenge, and going through descendants, nephews, in-laws etc might be an easier way to search connection than to bang your head on brick walls.
I don't know how you search records over there, so I will be of little practical help (unless someone finds a connection to France), but if I knew how to do it, I will try to collect low-hanging fruits : I see in the profile of his brother Milton that he married and had five children born around 1880s, with sources.
Why not add those, and push connections in any possible direction?