re: I'm considering building a woodburning brick pizza oven.

Big green egg does a pretty good job. I'm not 100% perfect at it yet though. Still finding that sweet spot where the stone is the right temp. Toppings always come out awesome. Bottom of the crust comes out slightly undercooked or slightly burnt as often as it comes out perfect. But that's me just not doing it enough. no problem with the grill.

OP,
Do you bake with a pizza stone in a conventional over? That's the first thing to learn (and to use parchment to move the pizza off of your piel until you decide if cornmeal is a good enough mover to go parchment less.

With you family celiac problem, having a dedicated oven outdoors might just work. Making other 'breads' in a single bake, enough for the family for the week would justify the heat up time.

But....this isn't something you sit by the fire and do and enjoy the flames. To build up the temperature, the oven door is closed..Sometimes it's metal, other times it's metal with several pieces of wood on your side of it. Building heat means heavy insulation to keep the heat in the oven.

As to cooking other things, temperatures vary, and from a high for bread to meats.... I would recommend Hubert Keller's cookbook Burger Bar for a phenomenal source for good foods that can (some of them) be cooked at high temperatures.

And then there's the cook in the oven after the burn is done and the heat is residual versus leave the wood on one side and the food on the other.

Making gluten free breads in a wood fired oven .....search out the cookbooks/baking books. That sounds really interesting. Especially using exotic grains that have no gluten.