Success was short-lived. Ran beautifully with rock-steady 14+ volts during a full weekend of camping, about 100 miles of driving. But as soon as I got close to home the gauge started slowly dropping again. Put a meter on it and sure enough, already down to 13.6V at idle.
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More research makes it sound like my problem is related to frying diodes in the alternator. I'm now going back to my original thought, that there's a problem with in the circuit involving the dashboard battery light.

As I said, with key ON, the dash light illuminates, but it is much dimmer than the other dash lights. It was dim even when I first installed the latest alternator.

We established that the 1 volt drop I was seeing at the white wire of alternator connector could be due to the power going through the 'generator relay'. That made sense, however, going the through that relay is kind of a backup/secondary path.

Wiring diagram shows that the power SHOULD also be able take the primary path, which is basically a direct shot from key to dash light to alternator connector. If that was working properly, seems to me I should see full battery voltage on that white wire, not 1 volt less.

When alternator is running properly, it applies voltage to the white wire. This is supposed to 'cancel out' the voltage coming in from the key/dash light. So +12V fighting with +12V on the same wire will result in net 0V at the dash bulb. Bulb has 'no voltage', so it then goes off to indicate the system is working properly.

But if there is a short somewhere in that white wire, alternator would essentially be sending at least some power straight to ground. My theory now is that this situation could be short-circuiting or overloading the diodes and causing them to gradually burn out one by one until all are dead.