Susie,
I empathize! I have trouble tracing my Scandinavian ancestors, so I wouldn't be any help. I understand how many name variations there can be, and how "-sen" often became "-son" in the US... and all the name changes that happened after immigration to the US.
Hopefully someone who knows how to read/search the Danish archives will be able to help you.
It might help, though, if you can provide the US state(s) where he was found on the 1900 and 1910 censuses. It really helps with genealogical sleuthing to have all the clues available. There are fuller source citations that are preferred on Wikitree, which you may not be familiar with yet, but that would be great to add to Christian's profile. If you can come up with the specific state, county, and date for the two censuses, I can try to help you with the sources.
Reba