Preheat the oven to 350.
To make the cornbread, in a medium bowl, whisk together the cornmeal, flour, salt, and baking powder. In a small bowl, whisk together the eggs, buttermilk, and oil. Pour the wet ingredients into the dry ingredients and mix until just combined. Pour the batter into a greased pie pan or cake pan, and bake 25-30 minutes, until a toothpick inserted into the center comes out clean. Let cool for 10-15 minutes. Do not turn off the oven.
While the cornbread is cooling, melt the butter in a large saucepan over medium heat. Add the onion and celery, and cook, stirring occasionally, until softened and translucent.
In a separate saucepan, heat the chicken broth, salt, pepper, and poultry seasoning, until warm.
Crumble the cooled cornbread into a large bowl. Add the stuffing cubes and saltine crackers, and mix to combine. Pour the vegetables and butter over the top and stir to combine. Add the chicken broth mixture and stir to combine. Taste the mixture and add more salt or poultry seasoning if needed. Add the eggs to the mixture and stir until blended.
Pour the stuffing mixture into a greased 9 x 13 pan. Bake 45-50 minutes, until set and lightly browned on the top.