Maybe the regulator is all screwy and took the battery out then, not really sure, can happen though and it can be more common if it's overcharging at higher RPM's.
I do have to mention this also. You mentioned you have a large stereo, but you're only running 1 battery. If that is the case I am finding the alternator as being overkill. It could be that the demand the stereo puts on that single battery and the reaction time for the alternator to up the amperage to the demand is sub par. Meaning that the battery is being heavily discharged before the alternator can kick it up, hence slowly killing the battery, and if it's a newer Optima ('04ish and newer) they have lost the great quality they once had and are now just a fancy name.
Also if this stereo is that large and the alternator is capable of keeping up, the power wire to the alternator should be up-sized. I wouldn't doubt if the fusible link is on its last leg and maybe causing a problem, it's the first 8" or so of the power wire from the alt to the battery.