Remember tainting is a microbiological process...think multiple and simultaneous fermentations. Microbial growth is temperature dependant. If you were to add your sodium benzoate, already dissolved in a small volume of water, stir well and rapidly cool the mixture you will stop things about as fast as possible. I have placed my buckets in a refrigerator immediately after adding the benzoate.
Sodium benzoate is a growth inhibitor not a metabolic poison. As such it must reach inhibitory concentrations in each bacterium before the “taint” is completely inhibited. These types of inhibitors tend to have a much more shallow inhibition curve than say penicillin, rotenone, cyanide or other nonreversible inhibitors.