Well that was a nice lengthy post, but once again you are promoting something that you shouldn't be!
I am going to try and sum this up as blatantly as possible, and I think that WiLL is leading you in the right direction.
A stiffening capacitor is not made to stop the dimming of your lights while playing high power audio equipment.
Yes, in some cases it helps the dimming of the lights because it stores charge.
"Stiffening capacitors are used as a sort of electrical shock absorber. As voltage starts to rise, the capacitor will absorb energy which will tend to keep the voltage from rising as quickly as it otherwise would."
If you want to correctly fix the light dimming problem on your high power audio system, upgrade your alternator. As WiLL said Honda doesnt really supply their cars with a very big alternator at all. They dont build the cars with large audio systems in mind.