As it turns out, most packaged products with soy cheese contain casein. This is unfortunately true of the soy cheese pizzas out there I was also hoping to try out with my daughter (for a good no-cheese pizza option, see this post). I suspect it's the casein in these soy cheese products that allow them to behave much like regular cheese, in particular its ability to melt nicely.
Anyway, I figured going forward any type of cheese would just have to be avoided altogether, that is, until I found yet more varieties of cheese at Whole Foods. We've since tried a couple of completely dairy-free cheeses, this time vegan ones and therefore devoid of any cow's milk product. The one that my daughter likes best is the Vegan American Flavor Soy Slices from Galaxy Nutritional Foods. I like the fact that these are sold as slices so my daughter doesn't feel any different from her peers who may be eating their brand of yellow sliced cheese (although you need to be careful not to get them mixed up). Note that these are also soy-based, but are clearly marked vegan. From the perspective of one who has always eaten cow's milk cheese, this cheese doesn't taste as great and it doesn't melt well. However, since my daughter has no basis for comparison and is quite happy eating her cheese slices, this ultimately makes me a fan of them too.