I want to share an idea I stole off a baking site, where someone baked the no-kneed bread on a baking stone with a 4 quart pyrex bowl as the cover instead of the cast iron dutch oven:
It's hard to use the dutch oven in the brick oven, since there's no shelf to pull out, and you have a hard time forming a boule-shaped loaf when you're dropping it in from above, particularly if your landing doesn't come out much beyond your arch.
You'll note that in the picture the pyrex bowl is propped up by a brick. This, and the oven thermometer, go in about half an hour after you've shoveled out the coals. When the air temperature is around 500f, you lift up the bowl with a hook type tool, and slide in your loaf off the peel. You use the hook to position the bowl over the loaf and drop it down. About half an hour later you remove the bowl, and continue baking until your loaf is about 200f internal by a probe.
I call this the poor man's cloche. As a bonus, it's a lot stronger than the terra cotta cloche.