You're in luck! Edamame are nothing more than 'immature Soybeans'. And Soybeans definitely grow in South Louisiana. I'd go to some Organic sites, to see which varieties of Soybean are recommended for a home garden in your climate. If there are heirloom varieties available, those would be the best choice, because they would be adapted to being grown by actual people...rather than by giant chemical-spewing machines.

Funny, but I was the first one to raise the alarm about Chinese-grown Edamame...at least at the healthfood store in South Louisiana where I read the label, a few years back, and asked the staff if they realized they had frozen Edamame from China, and how dangerous that might be. A few months later, of course, the whole scandal about Chinese producers and melamine...etc...etc...dominated the news. I was tempted to drive down there just to say "Told you so!"

You're smart to grow your own. Good luck!

Until we moved across the continent, we were 'subscribers' to an organic farmer's 'Vegetable Club' (we paid, at the start of the season, for a share of their production), and they gave us Edamame a time or two. Rather a bit of work, since you have to shell them, like you would Field Peas...

And while you're planting, try Amaranth Greens. They are dark red (related to Cockscomb flowers), with a strong flavor that's pure heaven in a Vegan Gumbo.

Bon apetit!