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.