About that 500F cooking temperature. . . .
At first glance it makes sense that a larger pan of batter would need a lower temperature, but I wouldn’t advise it . . . yet. I was a professional baker for a number of years, and I can say that I’ve (almost) never lowered an oven temperature when baking a larger cake (which is essentially what you have here). If the goal is simply to scale up to a larger diameter, it’s most likely unnecessary to lower the temperature—so long as you’re working with room-temperature ingredients and the thickness (height) of the “cake” stays the same. It’s important to remember that the heat in the oven surrounds the item being baked. As such, all sides are receiving heat. It may take a few more minutes to bake, but this recipe has no sugar and a (relatively) small amount of fat for a baked-good, and I wouldn’t worry about over-browning (even in a hot skillet) until closer to the end of the baking time. At that point, you may want to turn the heat down.
Looking at this recipe, I think the high heat is vital to the success of the bread. Why?
1. The reported age of the recipe. I would wager that when this recipe was first developed, the original baker was using single-acting baking power. Long before double-acting (which is what most of us are used to), there was single-acting powder. It worked by allowing an acid to react with a base in the presence of a liquid (sound familiar?); the result was a release of gas that would lighten the mixture. In essence, there would be an increase in volume (prebake) that is similar to what results when creaming butter and sugar. By baking in a hot pan and hot oven, the gases created by the baking powder (as well as steam) expand to leaven the bread. While double-acting baking powder works in a similar fashion, it only releases about 2/3 of its gas in the bowl; the rest is released as the batter heats in the oven. In a baked good with a large amount of wheat flour, the batter can accommodate this late-release of gas because wheat gluten stretches. Cornmeal batters, however, don’t stretch; they need the high heat to expand the gases before the proteins and starches set.
2. That small amount of flour; why is it there and why does it support my claim that high heat is vital? I don't think it's enough for structure; I believe it's there to prevent the egg (and milk proteins) from coagulating too soon. A beaten whole egg coagulates (sets-up, scrambles) at about 156F, whereas a custard (egg and liquid) will set in the range of 175-185 (above that, the egg will coagulate). This is why some recipes/ techniques for making scrambled eggs have milk added to them--it's insurance that prevents a novice cook from ending up with an over-cooked and dry breakfast. If we add starch to that custard mixture, we add even more protection; recipes for pastry cream and homemade pudding can be safely boiled without fear of making a coagulated mess. Now apply that to Arthur’s recipe: scorching oven, hot pan, shallow mixture--and an egg. Without that flour, the egg and milk proteins would most-likely curdle, and if they curdle, they will do nothing for the structure of the bread.
My advice: either take dixiedragon’s advice and make 2 pans (which, by the way, is some of the most sensible baking advice I’ve ever read!), or if you must bake it in a large pan, scale it up, and proceed as normal. About 10-15 minutes in, take a look and make an assessment. If it’s browning too much, turn your oven down—just don’t do it in the beginning!