I think what Hyde is getting at is there is more to the charging system than you are focusing on. If you alt is putting out 12.5-13.5 volts it may be just fine.
you battery may not be taking a full charge, but a problem that is common in older vehicles is cable decay. As the cables age the copper inside breaks down, at times you may even see a greenish crust form (a chemical known as copper sulfate). So what does this have to do with your alternator not keeping up with the load. I'm glad you asked, the degraded copper is not as conductive as good clean copper, thus you have the effect of lost "juce"
So for instance, lets us pretend 1 foot of alternator wire that is new has 1ohm of resistance, but a corroded wire has 2ohms (or twice the resistance of the original wire.
I hope some of that helped. I have been up all night sick and typing is quite the task for me at the moment.
it may very well be your alternator, and throwing a new higher output alternator in may very well fix any of the mentioned problems for now. But its worth testing the Alternator, battery and then Ohming the wires.
Good Luck