Jaypeg, did your 6” and 9” squares turn out badly? They are not so different from a 9” round- the smaller cake should have domed a little but otherwise been fine, and the 9” square should have been Ok or maybe just a tad sunken in the center. Did you try to bake them in deeper layers, or change mixing times, oven temp, or flour?
For any size layer, don’t increase the depth (no 3” pans).
For the 12”, it gets tricky. Definitely use a heat core or Patrincia’s trick of a flower nail in the center to help conduct heat. To get the same mellowness of flavor as in the regular recipe, you will need to increase baking soda proportionately along with the rest of the recipe, so that the sour cream is neutralized to the same extent. However, to strengthen the structure enough to hold up across a larger pan, you will need to reduce the baking powder.
So the calculation for two 12” layers needs to go something like this:
1. Increase baking soda proportionately with the recipe (for example, if you are multiplying the recipe by 3.5x, which looks about right, use 3.5x the baking soda, or 1.75 tsp)
2. Find the baking powder equivalent of that much baking soda (in this example, 1.75 tsp baking soda has equivalent leavening to 7 tsp of baking powder- multiply soda by 4)
3. Check the charts in the back of the book to see what the correct amount of baking powder is for your 12” pan. According to the recipe on p. 484-5, it is 7.75 tsp. Or, you can multiply the rose factor of 7 by the baking powder level of 3 (1.125 tsp) to get 7.8 tsp (explained on p.489).
4. Your pans are square, and so may need slightly less leavening because of the additional space in the corners. Perhaps round down to 7 tsp.
7 tsp is the exact amount of leavening provided by your baking soda, so you could try just eliminating the baking powder all together in a 3.5x recipe of the sour cream butter cake. This would appear to be the largest cake that can be made from this recipe, because any larger and the required amount of baking soda to neutralize the sour cream would over-leaven the cake. I am not sure if the 1/2 tsp reduction is the right amount to compensate for the corners in a square pan, it is possible that the cake will still be a little over-leavened even without any baking powder.
Editing to say, oops, I just noticed the dates on Jaypeg’s post. Oh well, maybe it will help someone, somewhere…