An amp with a high damping factor will need a resistor in-line before the capacitor.If the cap across the tweeter doesn't fix it when I try it tomorrow, I'm down to move to the next step. If that's a DSP, give me a recommendation for an inexpensive yet decent one!
If it is the amplifier that is hissing like a pit of vipers, then a DSP will not help.
ideally one probably wants to understand what is happening before just throwing a buchacci of solutions at the problem hoping one of them sticks to it.