OP, I also have a Centipede lawn in the Florida Panhandle. How long have you been at the property, and how long has it been predominantly Centipede grass? Is the area of your lawn which is struggling getting enough water/irrigation? The recent drought in this area has posed some challenges in my yard with thin spots.
The 15-0-15 you used is probably adequate, especially if its got some of the micronutrients added that your yard is lacking. It will likely take at least a full growing season and re-fertilizing before the overall soil test numbers improve.