UW and EWU don't conduct interviews, so you really have to stand out on paper. But you never know until you try. I had better luck going east. Hope that helps.
Also I wouldn't worry about Ws. In fact they don't even look at transcripts really other than the actual numbers (overall GPA, pre-req GPA and sometimes last 45 semester credit GPA). I had a 3.6 overall and lower in pre req and still got accepted to multiple schools. Just don't take the personal statement for granted.