I had the battery tested at the local Autozone. He put it
through a load test and proclaimed it to be in excellent condition.
(The voltage was over 12 volts.)

You took a battery off the charger, hauled it to Auto Zone, and the kid behind
the counter said it was OK because it showed over 12 volts?

You should be at 12.6-13.2 with a fully charged battery. One very weak cell
sounds like a distinct possibility. Most batteries "fail" when a single cell
goes bad.
That's why I now have batteries built from
individual, replaceable cells. When one bites the dust, you replace the cell-
not the whole works.