When I plugged it in to my charger the 100% light was flashing, the next lower light is 75% so all this tells me is it was between 76-99%. When my charger said it was 100% I took it to Autozone and their tester also said 100% so I'm now confident my charger does work properly and can charge it completely, making some progress.

While it was charging I've been doing some thinking and have a theory:

This is just a THEORY, PLEASE DON'T HESITATE TO SHOOT HOLES IN IT!

Couple things I'm certain of:

1. I know there was something wrong with the battery
2. Our cars have an Intelligent Battery Sensor on the battery (IBS)
3. The output of the alternator is controlled by some module and not a simple voltage regulator.
4. When installing a new battery you need to reset the charge adaptation in INPA.

When I read 12.x volts with the car running my old school brain tells me the alternator is not working, but what if instead of not working or deactivated as the new cars do, it's actually working just not trying to charge the battery.

It would work something like this:

When the system is charging the battery it knows the alternator output voltage and via the IBS it knows how much current is going through the battery to charge it. As the battery voltage rises the current will decrease and eventually plateau when that battery reaches it's maximum charge. As the battery ages the max output voltage decreases. Let's say for a specific battery it now at 12.5V. The car will remember that and when it gets back to 12.5V it will reduce the output of the alternator to 12.5V. At that point it will no longer be trying to charge the battery (better for battery) and it will be the minimum load needed on the alternator to operate the electrical system (better mpg).

There would also be an amount of hysteresis to prevent the alternator from constantly turning on/off. Lets say it's .1V, that would mean on my example above that the voltage would be allowed to drop down to 12.4V before the system would kick back in to charge mode and the alternator would put out 14.x volts until the battery was brought back to it's max of 12.5V where the system would kick back in to "cruise" mode and only output 12.5V.

This would explain why I'm getting reading that seem lower than expected and also why it's necessary to reset the stored battery info when installing a new battery.