My concern about broadcloth is that invisible machine applique may not be sufficiently invisible on it because of its weave. I will be using a fine needle, and I just think broadcloth is going to be too coarse for this project.
Mottled fabrics are not out of the question. Most of the applique fabrics will be batiks, so I want to keep the background very subdued in order to highlight the applique fabrics. That's why I do not want to rule out solids. It's just that, with the exception of muslin, all of the solid color fabrics I am finding are broadcloth.
I might end up looking for a very subdued light-colored batik, but it is almost impossible to find a good selection of these in quilt stores, and buying online without a swatch first is risky -- especially since I will need something like 7 yards.