It kind of sounds like the alternator again. Do you have a multimeter? I'd check the battery voltage and then the voltage at the alternator, the alternator should have a higher voltage (< 1 volt) then the battery. You can also try and unplug the battery as the car is running and see if the car still runs...
Although I do not know how well these things will work on the older cars, especially running the car on the alternator alone, I know a lot of guys here (I believe) do not like this test.