I know this is fairly old but since no one has chimed in I thought I would. My family is gluten free and the NFSC was our favorite recipe before we went GF. We still use the NFSC recipe but I use Bob's Red Mill Gluten Free All Purpose Baking Flour (most grocery stores near me carry it so hopefully you can find it.) Along with that we add Xanthan gum to the recipe. We just did a double batch of the recipe and used 2 tsp xanthan gum and it worked out pretty well. The Bob's bag will tell you how much to use but when we followed their directions we found the cookies to be a little bit too tough for our liking. Play around with it and find a ratio you like. You don't have to use Bob's either, it's just convenient for me since I can buy big bags of it at Cash n Carry. If there is a mix you can find locally try it! Or there are many all purpose GF flour combinations online that you can mix up yourself.
One word of caution on the Bob's, it's got a garbanzo bean base to it so it will not taste very good raw. Trust me on this one. But once they're baked they taste pretty darn close to the original recipe and once you have frosting or a glaze on them you really don't know the difference. You can roll them out using a little rice flour or just use whatever you used for the AP flour in the recipe. Just make sure it isn't gritty at all or your cookies will end up gritty (some rice flours can be like that). You can PM me if you have questions.