Huh, thanks for the clip. She was speaking to someone from Russia in the video, so the pronunciation may still be a little different from the Polish. Also, she seems to pronounce it with a more American accent, when I have a feeling the Polish pronunciation lies somewhere between "ZAH-sha" and "ZOH-sha," so either one is close enough in my mind. I'll have to ask my neighbor down the street from Poland how exactly he pronounces it.
I like the supposed Polish pronunciation best, but as far as English approximations, I'm fine with ZOH-sha.
I think pronouncing it as ZOH-see-a is fine for a middle, but I think that would be a point of confusion if used as a first name.