Thinking of slicing my cheese like they do ( I know Scott123 cautions me!).
Mark, Grande/Grande clones have superior meltability, so, if you're using Grande, then it might be more forgiving of slices, but I think the most critical aspect of this approach is that the slices are as thin as potato chips. At the moment, I can't think of any home equipment that will achieve this. A food processor definitely won't, nor will a box grater. If you have access to a commercial meat slicer, then that would give you the necessary thickness- the square slices you get from using a grande loaf and a meat slicer work well.
Whatever you end up with, make sure to test it side by side with grated mozzarella. Make sure to bubble/brown the two pies as equally as possible and compare the taste and appearance between the two.
Sean, the larger the piece of cheese, the longer it takes to melt. Grated cheese melts far more easily than sliced. Sliced cheese, because of it's melting impairment, will have a greater tendency to brown rather than bubble, oil off less, and produce an end result that's less buttery and flavorful.