Gums will help a bit, but these sorts of recipes really can't just be substituted for and have them turn out. You need to decide what kind of cornbread you want. A cakey Northern style or a dense heartier Southern style. Norther styles use about half flour by volume and would be harder to replicate without gluten. Southern uses less to no flour depending where you are in the South and would probably be easier.
To some extent, baking soda can cover for eggs in that it provides the pH of the egg white and possibly some leavening as eggs often do.
The flour, you should look at the non-gluten flours to provide the extra volume and texture modification you're looking for.
A few popular alternatives include brown and white rice flour, coconut flour, almond four, potato flour, and chickpea or garbanzo flour.
And you're going to have to make a few batches while TAKING NOTES of your modifications each time to work toward the result you want.