May I suggest something you'll likely ignore?
1. Have your ecm tuned (preferably, your ecm AND your tcm, in person / on site)
1a. Among the many other things that should normally be addressed by a tune to suit your particulars, have your four idle RpMs - Park/Neutral, & In Gear, with AC On, and with AC Off - raised by at least 100 RpM.
The extra RpMs at idle would likely have been enough to make even an OE alternator put out just enough extra juice.
there's a whole alternator section in the tune as well. lots of stuff in there that should over ride the idle settings when voltage falls because of load, some kinda boost mode.