@WalterG, I ate the last of my delicious cornbread for dinner tonight. I have made it with butter, olive oil when I want to flavor it with rosemary, or canola oil when I am budgeting. You could certainly use corn oil if you like.
Tonight's cornbread had a couple of large (4") jalapenos chopped fine and stirred into the batter. If you want to substitute canned corn, first let me recommend thawed frozen corn as an alternative because it will taste fresher, and possibly be cheaper. I get a pound of it for 99 cents. If you're using a recipe that was specifically developed toward adding canned creamed corn, if you substitute corn kernels, you probably would have to up the liquid. However, if you are using a regular cornbread recipe that's designed to come out moist without inclusions, you could probably add corn kernels and leave the liquid at the same amount.
All my cornbread recipes call for a 425 F preheated oven, including my favorite, arrived at over decades, which I'll give at the end of this post. Three seventy-five is not hot enough, but if you absolutely had to you might get acceptable results if you increased the baking time. It won't be optimum. I think the reason your cornbread is collapsing is because it just isn't done. It's risen but not set. Longer baking might correct the problem. Cornbread should be moist but not doughy, and definitely should not collapse like a fallen cake.
Are you preheating the cast iron skillet along with the oven? If not you are setting yourself up for disaster! Cast iron accepts and then releases into the food an amazing amount of heat. If it's not preheated, combined with your reduced 375 oven temp, it's going to insulate your batter, and inhibit proper cooking.
Baking soda is wasted if you are not using buttermilk or some other acidic ingredient. Baking powder is baking soda and cream of tarter, which is acidic, and that's what allows it to work, but soda can work if you use molasses, vinegar, lemon juice or another acid.
adapted from Perfect Corn Bread
from: "Better Homes and Gardens New Cookbook", copyright 1968
Preheat oven to 425 F 
If you are using a 10" cast iron pan, throw it in the oven when you turn it on, and just before pouring in batter, melt butter and swirl to coat.
2 eggs
1 c milk
3/4 t salt (I like 1 t, especially with vegetable inclusions)
2 T sugar (they say 1/4 cup, but I dislike sweet cornbread)
Beat these ingredients together in medium mixing bowl. I use a hand whisk.
1/4 c shortening (not in mine)
I never use shortening, so if I'm adding a liquid oil, I substitute the same amount, and whisk it in with the other liquid ingredients. If I use butter, I make sure it's at warm room temp and add it with the dry ingredients, which follow. Add to your bowl:
1 c all purpose flour
1 c yellow cornmeal (I like stone ground)
4 t baking powder
Beat again until just smooth. Do NOT overbeat. Pour batter into pan and bake for 20 to 25 minutes. When it looks risen and golden brown, test with a toothpick in the middle. Toothpick should come out clean, dry and be quite hot to the touch immediately after pulling it out.
I like to use a heavy steel non-stick 9" Wearever cakepan for my cornbread and just spray it with an oil spray like Pam, but I buy the bargain brand.
It's never failed me, and I hope it works for you.
I also think I have a cornmeal yeast loaf recipe kicking around, so let me know if you'd like it, but I suggest you try this one first.
You've got one of those damned electronic ovens, don't you? 
