Yeah... wow... what a thread. Maybe it's my fever, but not one word of it made sense... and I don't understand what we are to be speculating. A lot of names have two origins. Consider the country of Georgia and the state of Georgia. Both names are derived from completely different sources, yet they are spelled and pronounced the same. Cool how that works... Anyways... so it's no surprise that there are two possible meanings for Katharine. Plus, the fact that there are several spellings could be the sign of a significant difference.
I'm all about choosing a name with a nice meaning, but just because a meaning doesn't suit you doesn't mean anything. I've known some Chastitys who were dreadfully misnamed. A moniker is a moniker, and that is that.
But anyways... I didn't mean to get involved. Sorry if my response is confusing at all or completely irrelevant to the topic, because I really am sick and I fear that I misinterpret a lot on days like these.