I can't tell you whether it is or is not possible to fit your body type--there may a brand out there for you. But I feel your pain.
I can say that I've mostly given up on crisp collared shirts at least for work-wear, because I never think they look neat and right on me, either. I can't really explain it since I can find my size, they can fit slimly and generally right, but I'm so long-waisted that if I tuck there's just too much space open for fabric bunching and pulling and it just doesn't work. If I try to layer, my sweaters bunch up over a crisp fabric if they fit me well, or if I go for a looser look I look like I'm in a sweatshirt.
Plus for some reason, in my current decade, shirt collars don't look as good. So I still want to have some "blouses" and not all knits, but I have crossed cotton/cotton-poly "shirts" off my list for now and look for more drapey fabrics.
You could try looking at tailored "knit" shirts and go for a good fit in the shoulders but have some give elsewhere, or look at silk or silk-like fabrics that may have some shoulder-shirring or something.
