What if the weapon has 2 of the "near" same? An old shadow price I got had the perks "reload faster after a kill" and "greatly increases reload speed on a precision kill". I used it just incase but was never sure that it stacked. (I KNOW it didn't stack with gunslingers reload perk though)
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The only thing I can suggest is try it both ways and see. Normally the perks give enough of an individual bonus that you can tell if they stack or not.