You had mentioned to me that your battery cables were loose. How about the little black wire coming off the negative battery terminal. Is it solidly attached to the battery tray?
I don't know what thread you found, but some recommend removing the alternator from the top. I wouldn't try that method. You're lucky you have a manual transmission. Swapping alternators on an automatic is a major undertaking.
Just be sure to disconnect the positive battery terminal before starting the replacement. The rest can be accomplished pretty easily from the bottom side of the car. Once the bolts are removed, you can maneuver the alternator out. Check the number of ribs on the pulley to be sure they're the same and be sure to replace the metal shield onto the alternator.
Regarding your PFF question about the AC belt---It doesn't have to be removed or loosened. Just loosen the alternator adjustment bolt, relieve the tension on the serpentine belt and slide it off the pulley. Leave it hanging on the other pulleys.
