I'll see if I can help a bit here. Not all the things I grow are heirloom, but they do grow well for me in this hot/humid climate.
Right now I have Creole, Black Krim, Cherokee Purple, Julliette Plum and Green Zebra tomatoes, with the majority being Creoles.
For peppers, I am growing Jalapeno, Hungarian Yellow Hot Wax, Sweet Banana Peppers and Bell Peppers.
For beans, I am now growing Japanese Yard Longs(pole beans), have grown Kentucky Wonder pole and bush beans, Purple Pod Pole Beans and for Edamame, I grow Envy Soybeans twice a year.
I love Okra and every summer have about 30 Clemson Spineless plants.
I grow many greens in the fall and some of them over-winter and last until summer. I use 2 types Swiss Chard, Fordhook Giant and Bright Lites. Lettuces usually consist of Black Seeded Simpson, Red Oak Leaf, and Buttercrunch. I also grow a Mesculin Mix of bitter greens, some Arugula, and Dwarf Blue Curled Kale.
I plant Georgia Collards each fall along with Brussel Sprouts and Broccoli and enjoy a bountiful harvest with these. I can't remember which variety of Sprouts and Broccoli I planted this year but they produced very well. I should keep a journal since CRS is creeping in.
Here's a couple sites to see what they offer in Heirlooms. El Dorado Heirloom Seeds, Seed Savers Exchange and look at this site for more info-----LSUAgCenter.com for a Planting Guide for our area.
Hope this helps a bit.