This year I am experimenting with vernalizing some of my garlic stock to see if that makes a difference in this warm area. I'm also trying two new-to-me garlics in the garden, Russian Inferno (Asiatic turban type) and Siberian (marble purple stripe turban), along with the Maiskij and Shilla I've been growing the past several years.
I found a small garlic company, Keene Garlic up in Sun Prairie, Wisconsin that was willing to ship mine as early as possible to give me more time to pre-chill the garlic.
He sent me a list of what he had growing, some of which isn't in his online list yet and from that I was able to look them up and find the two I thought might do well here.
https://keeneorganics.com/
So into a paper bag and into the veggie bin they go for about 10 weeks until mid October.