You will never get as high a rise out of cornbread as you will with other quickbreads which are primarily wheat flour because there's less or no (depending upon if your recipe uses wheat flour) gluten structure. The lack of structure is why you see the rise then fall; air bubbles, kind of like balloons, are formed but the batter can't maintain the bubbles/balloons beyond a certain point and they burst. (This also happens at high altitudes with all sorts of baked goods.)
None of your add-ins help build structure. Some of them are hindering your project.
An additional egg will help a bit, but it will also change the texture. Using a small amount (maybe 2oz) of high-gluten flour will help with keeping the rise, but will also make a tougher product.
Using finely milled corn flour as opposed to cornmeal gives a lighter texture. It doesn't help structure, it just gives a less dense result.
You could try yeast, but, you will get similar results (with an added yeasty flavor) because yeast doesn't affect structure much beyond consuming a microscopic amount of starch.
Overall, I'd say stop using so much leavening, it adds bitter, bad flavors. With less leavening maybe you'll be able to tolerate more simple cornbreads, without so many non-corn ingredients. Essentially, you need to accept the fact that cornbread will never soft and fluffy like commerical white breads.
