Been awhile since I've posted here...just wanted to share some of what's been happening in my quest (to be able to make a GF pizza that looks and tastes almost indistinguishable from a regular NY pizza that you'd find in a NY pizzeria).
First, a quick and perhaps obvious finding--it's pretty much impossible to succeed with just a store-bought mix alone. There are good ones and bad ones, some are better than others (I liked using Bob's Red Mill Pizza Crust Mix for a while), and I've tried just about all of them--but you just can't get the Holy Grail using a pure store-bought crust and following the recipe. It just ain't gonna happen, so give up that idea.
Second--I found a recipe that seems to get pretty close! Full props and thanks go to "cymry-pa", on whose blog I found this recipe, which I've modified slightly for my own uses (I use less yeast and a tad less dry milk powder):http://cymry-pa.blogspot.ca/2011/01/new-year-new-kitchen-adventures.html
The basic concept here is that it uses Gluten Free Pantry's french bread and pizza mix, and then (here's the key point) adds dry milk powder (in a fairly high proportion). That is what gives the pizza its light fluffiness, a better taste, and helps it get a nice browned char on a pizza stone. I've been preparing the dough in a pan, baking that for a few minutes next to a preheating pizza stone in the oven, then transferring to a peel, and from thence to the pizza stone. Key factor--HIGH HEAT. I turn the oven to its highest (only 500 unfortunately) and then I calibrate it to fool it into thinking it's 30 degrees too cold...so I get a total of 530 degrees max. This actually works relatively well (although I wish I could go to 600!). The pizza comes out with a nice crunchy browned bottom and has a bit of char to it. The taste is fantastic--VERY close to a regular NY pizza.
I'm in the middle of trying to replicate that recipe using regular GF flours rather than buying the mix in a box. The GF Pantry mix uses mostly white rice flour, corn starch, and potato starch, which is a fairly common GF mix to use, so it's just a question of experimenting with different proportions to come up with something pretty similar. I'm also trying to add a slight amount of brown rice flour/bean flour for protein/fibre, and also some sorghum/tapioca to create a more nuanced taste. Haven't hit quite upon something I'm totally happy with yet, but I'm getting pretty close
One last thing I've learned is to use excellent sauce and cheese ingredients. It only makes sense--if the crust is going to be subpar just by its GF nature, then you have to try to make up for it with outstanding quality sauce and cheese.
I hope that's all of some use to you amateur GF pizza makers out there
Keep the ideas coming!