Here are some of the cajons I have built. Used birch plywood and also some are pine, 1/2" with 6 ply 1/8" heads like fat congas. On the large super tumbas (24" tall, 15x15"), I use 1/4"....
i think i might have to experiment with a supertumba cajon that is bigger than 15"x15" at the top. My biggest is 15"x15" but i'll bet the bigger one has a nicer bass tone. Here is how my big tumba cajons sound: