Yes, there are certainly GF flour substitutes, so in principle I suppose I could do that. But the nice thing about buying them is that they keep indefinitely, so I don't need to faff about preparing a base the day before I plan to be in a pizza restaurant.

Also it's interesting that you say it's easy, because my mother spent quite a lot of my childhood trying to find a good pizza dough recipe, and although she eventually came up with something that the rest of the family was happy to eat, it was never quite to my taste. So I was left with the feeling that making pizza bases was more subtle an art than it looked. I'd ask for your recipe, but it'd probably need extensive modification to work with GF flour anyway.

I suppose there are three possible conclusions we can draw

a) I can cook far better than your mother.
b) I have a lower expectation for Pizza bases.
c) I, by accident, found an ideal Pizza recipe.

I doubt a) or c) are likely hence we are left with b). One thing that might suggest the bases aren't too bad is that I make them with my automated bread maker (rather I make the dough and then roll it out myself) so it is more sorft and bread-like than one that one might make by hand.

WRT the keeping problem, they can quite easily be wrapped in cling=film and frozen. Then the problem reduces to remembering to take it out of the freezer in the morning.

Rich, why don't you try getting some gluten-free flour (+ whatever else is needed to replace normal flour) and seeing what happens to the recipe? It'd be an interesting experiment.

True, the other possibility is to create not-quite-pizza-bases. For example we often use Naan breads or french-sticks as bases which work nicely. Perhaps there exists some GF product which could be co-opted into being a base.