As an update:
I swapped out the battery yesterday and the battery light disappeared... for a day.
It came back on this morning, but instead of coming on during a heavy load, it came up just before I was getting on the highway and stayed on for about 7 miles. Then it went away and didn't come back on. Confusing.
Either way - I'm done dinkering around with it. The new alternator goes on tomorrow and with any luck, this problem will be a memory.
Thanks again, Ray.