I can see the basis for your belief that a broader peak (more total energy) is will do more damage but as I said, I'm unaware of data to support this.
More particularly, I doubt there is any evidence to support your integration rule. You'd be a brave man standing up in court trying to defend that
As for how much peak reduction a given personal hearing protection device will give, you will be making a bit of a guess there too. The reason is that attenuation is often non-linear, in some case very definitely. As an example, I occasionally have made for clients custom moulds into which I fit a non-linear filter. This particular filter (originally designed for the Aussie Army) provides very little attenuation at low inputs but becomes progressively more effective at higher inputs. The basis for this is feeding sound through a very small aperture - "turbulence" clips the peak, the louder it is.
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