I agree with an ellipse, but not exactly how you have drawn it.
I would think the foci of the ellipse would be F1) approximately the center of the fire and F2) approximately the center of the baking pie (such that the edge of the pie is a couple inches off the wall).
Keep in mind that the foci of the ellipse are on the deck - not on the plane across the top of the soldier course. The soldier course truncates the edges of the ellipse, so you are only building the top part of the ellipse which looks somewhat like your "half lens" design.
In the drawing below, the dome height is H1, however, arched portion of the dome is only H2 = H1 - soldier height.
(Illustration not to scale)