The shop where I work just got in two bolts of fantastic muslin! It's very high quality...Moda muslin, both bleached and unbleached. Doesn't look like any muslin I've seen before. And, it's not too pricey, retails at $4.99/yd.
However, I'm not sure if it will help with your shadowing problem. Perhaps the white on white you are using is substandard. I never buy Walmart fabric anymore. It's just not good stuff and if I'm going to invest all that time in making a quilt, I would like it to last as long as possible.