Pil, I think your idea of a belt is spot on - camel with rivets/studs sounds like a good choice to have on hand. I can't stand stiff shirts either - I found a soft light "denim" one at BR year before last, and I think they might still sell a version of it - not as dark as pictured but it is a deeper color than chambray so I guess it depends on what you want for color.
I'm wondering if that skirt is just a bit hard to style though - so I guess if it were me, I wouldn't try to buy anything specifically for it for fear of building around an item that is challenging - I think I would choose to keep trying things I have and things I just want anyway, and if something does work out with the skirt, fine. You know what I mean?
That said, a V-neck banded bottom linen sweater or knit (3/4 sleeves or long sleeve) seems like a great option for that skirt. If you are in the market for something like that, maybe it would work with it...
I have to admit it is fun to try and do imaginary shopping for others.