Hi,
It is my understanding for baking cakes and cookies, you do not want your convection status on.
What I observe to be the biggest issue for making this sheet cake in a larger pan is how long do you need to bake it. There are timing differences between 8-inch, 9-inch and sheet cakes. Some years ago I made a 4-tier wedding cake for a friend. I used a white cake batter and obtained information from the Joy of Cooking on how to adjust cooking times to the pan size.
You also asked about chocolate over carrot, carrot is usually a denser cake with lots of additions (coconut, grated carrots, raisins or chocolate). I have Cook's Illustrated but I don't have that issue to look at right here. If there are a lot of additions, as I suggested, then I would stick to the size pan recommended in the article or switch to a simply chocolate cake and read Joy of Cooking for timing. Since you have a wide oven, you could make double batchs of batter and divide it between two pans to speed this process along.
Baking cakes is more chemistry than anything else. When you change variables (pans or ingredients), then the outcome changes if there are no adjustments.
As for the quantity of cake pieces, pull out a ruler and decide how you want to cut it up.
Have fun!
Regards,