I suggest you consider having a soil test done of the soil in the problem spots. Perhaps some nutrient is way out of balance. Most of what you mentioned should have helped. Liming should not be needed for centipede to be happy.
I also suggest you take a photo of the turf and a 4" X 4" sample of sick, not dead, turf to your County Extension Office and see if they can identify the problem and if necessary prescribe an appropriate remedy.
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