For wiki hosting, I personally like Wikispaces.com; it's free and has an easy to use page editor.
Just Checked it out, looks reasonable but the overall layout itself, down to the core looks a bit like a 'wikia' site style, not so much for posting large amounts f information and links but more for page search and basically an aesthetic look. -Please feel free to correct me if I'm wrong
Would it be possible to be able to simply "freeze" the old wiki once we hit the next week and then start a new one?
Feasable yes, but of course there are still species which will be extant for many generations, it would be quite an annoyance to jump back and forth to find a species you want to evolve and more of a hassle to link the evolution's on the new wiki back to the old one.
I don't think we have the man power to move everything over manually. We need to find a way to upload all the data from the wiki at once
Yes as AnguaNatalie was talking about, if there are import and export functions it would probably be good to see if that can move large chucnks of data of page by page. Rewriting everything from as far back as Protosagania would be a last resort