alternator issue 2005 nissan sentra

I was listening to my stereo with the car idling and when I turned it up to a loud volume the radio shut off and the headlights blinked. I turned the radio back on with the volume lower and everything seemed fine. However, when I was on the freeway heading home the radio started to turn off and then on and my headlights and dash lights blinked each time the radio came back on. The volume was very low so there shouldn't have been too much current being drawn by the audio system. When I got home I checked the voltage at the battery with the car running and I got a reading of 13.9 volts. I then connected the DMM to the alternator and the reading never went above 14.04 volts, however, when the cooling fan turned on the voltage dropped below 12 volts and the car almost stalled. I turned on the AC, brights, and hazards all separately and each time the voltage dropped below 13.5 volts (sometimes below 13). The battery is new (Stinger SP1000) and reads 12.66 volts when the car is off so I am sure that it is being charged. I know that I will eventually need to upgrade the alternator due to the demands of my audio system, however, does the problem sound like the alternator could be dying now? My audio system has been installed for two months and, until now, I have not experienced this problem. I have read a lot about the Big 3, however, 1/0 in a Sentra is going to be a stretch. The wire from the alternator to the battery fuse enters a fuse box that would not accommodate a wire of that size. Any tricks of the trade for getting it to fit. I have a long commute and I do not have a desire to be stranded on the side of the road so any advice that you could provide would be greatly appreciated.

go get a batt and load test @ parts source of you rlocal shop its always free anyways. see if your alt is holding up or it could be your batt eventhough its new.