As the owner of a good JL audio setup in my other truck I can vouch for the experience.
Number one, yes, the alternator is weak, upgraded windings aren't too expensive at an alternator shop.
Two, I wouldn't waste money on a capacitor, most of the are only 1 farad, will cover you for the initial drop and a faster recovery time. However, if you don't want any dimming at all go with a bat-cap like these kinetic ones.
Kinetik High Current Power Cells
You should only need the smallest one, these things are superb! It'll wire in just like a cap but will resist dimming much better.