Answer: 'Chandler' is the best bet for your area. 'Camerosa' and 'Sweet Charlie' are other good options. All 3 of these are best grown in the annual system: plant in October, fruit in March through May, remove plants and use the space for other things until fall.
The perennial system in which plants are kept for several years is not as successful in the deep south because summer heat, diseases, pests and weeds must be fought for months on end, and the patch tends to decline after the first year. If you are determined to keep it going, I would suggest you dig up your best "daughter plants" in October, rototill the rest into the soil along with some added nutrients and reset the daughter plants. Water them lightly 2 or 3 times a day for a week after planting to get them off to a running start!
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