rice slayer' -- actually, a bigger alternator could cause an even greater drop in available horsepower. As you crank up your system, you create a high demand for current. As the alternator is asked to make more current, it will in turn work harder. This extra work is at the expense of available horsepower. You witnessed this first hand by having your system disconnected, therby lessening the demand of current from your alternator.
Like anything else in your 'stang, you should be sure your charging system is working efficiently. Large current requirements of a multi-amp system call for large cables to minimize resistance of current flowing through the wire. In addition, your vehicle as equipped stock hasn't the necessary return path for all of this current -- yep, you'll need to upgrade the ground cable from your battery to chassis, add one from the case of the alternator to the chassis, and insure your amps are grounded to a spot that can indeed flow the kind of current your system requires. I would also insure that your 1 Farad capacitor is installed very close to the power amp it supplements. Keep in mind you'll drastically reduce its' effectiveness by trying to use it to store charge for multiple amps through some kind of distribution block. Finally, I'd be sure you've got a fresh battery under the hood that has been designed to be deep cycled hundreds of times before its worthless (Rockford Fosgate, Lightning Audio, and Optima offer these).
All of these things can lessen the load on your alternator as they will make current delivery to your system more efficient, therby freeing up some horsepower.
