sorry folks. the point that is being missed is:
the OP makes a recipe.
that recipe make a given volume.
that given volume of batter does not change whether is is poured into one 9x13 pan or two 9x9 pans.
“why are you assuming that a 9” pan would be less full, i.e. thinner batter, than a 9x13?"
I’m not; he assumption is, per the OP, two 9x9 pans.
the OP clearly states the recipe calls for a 9x13 pan, and the OP wants to use two 9x9 pans, and it worked. the assumption that the volume of batter such that half the batter will not fit in a 9x9x1.5, and the remaining (more than half) will fit into a 9x9x2 pan, thus making the baking time shorter / long / different is completely outside the discussion. if the point is to make assumptions to prove some theory, then I’m going to bake the cake in my Tardis, because it is bigger on the inside than the outside and all these issues go away.
the question is not about the volume of the pan(s) - the length, width, depth of any or all of the pans does not change the volume of batter created by the recipe.
the definition of volume is area times thickness: V = A x D
I don’t know how the new math works, but in the old math if the volume of batter stays the same and it is spread out over a bigger area, the thickness must decrease.
- and two 9x9 pans have an area of 162 sq inches vs one 9x13 pan with 117 sq inches.
