Do you have the original equipment alternator with an external regulator, or has the alternator been upgraded to the later internal regulated type? The older system with the external regulator was notorious for diode leaks and the exact symptoms you're describing. I'd recommend trying another alternator before doing anything else. If you choose to isolate the alternator charging wire, don't run the circuit through the ignition switch- - - -use two Bosch-type 60 amp relays wired in parallel and energized by the ignition switch to be able to handle the alternator current without an excessive amount of voltage drop. Even that will be a band-aid fix, however.
Jerry