I currently have a similar issue with the name Cullom in my tree, no idea where it fits and very confused. So I found the party they all seemed to have in common - which is Francis Tilman Cullom(or a variety of names) and I'm working my way down from him as time allow until I can find places where his descendants seem to pair with my tree.
So far I haven't found the magic clue, but I'm starting to think I've getting a false positive for the "projected" relationship, based on potential lines crossing in the Deep South - And I've been working on triangulation to prove the lines up .. which is a pain in some places like DeKalb Tennessee as finding a "pure line" is so hard in some cases..
It appears I've got them in Common with a paternal grandmother's cousin, but in the tree just found his descendants married into my paternal grandfather's line.
As for the Australia, that may be a red herring, I'm in Canada, my son was born in California and he's now moved to Australia and had my first grandchild.
With our current Global moving around, people who are stationed in various military bases around the world that I'd focus on those brick walls - as I think this mystery line will solve mine.. it's just linking him to one of of the 4 that I think he might -