I find this a really interesting question!
I realize that the others have given you great suggestions about how to wear the shirt, but I think that no matter what you do it it, it's still a fairly traditional look. Is it possible that you just don't respond to this particular type of look, no matter how you style it?
I have not worn any type of woven shirt in probably 20 years, for several reasons. Apart from the fit problems, I have never really liked anything with a collar. Collars always felt stiff and confining to me. it has always seemed to me that knits were hipper looking.
However, suddenly I've become drawn to all these completely different looks than I'm used to, like the woven shirt. In fact, I have now become obsessed with them and have been trying them on everywhere. I actually bought that Eddie Bauer shirt you have and I love the fit. I also found one from Jones NY that has the same open collar and fit me pretty well.
I'm starting to want them in different colors and even stripes! (I have never worn stripes in my life!) I bought one from Eddie Bauer that's a black and white print - I wore it under a black jacket and I LOVED it. I suddenly LOVE the look of a striped shirt under a blazer. I'm still not really good at the whole cardigan/layering thing, and I think I prefer the structure of blazers over sweaters anyway, but I'm experimenting like crazy.
To me, the woven shirt feels very different from the knits I'm used to wearing. It feels more structured to me, which for some reason I am really loving right now. You couldn't drag me into a woven shirt for years. Now, I'm suddenly obsessed with them!
I guess what I'm suggesting is that maybe the classic button down just isn't "you," at this point, no matter how you wear it. Do you think that's possible, or do you think it's just a matter of finding the right way to wear it? Or maybe it's the fact that it's plain white that's not "you?"