Well, I was using 5.0v in my calculations from the reader, and I was under the impression that I was getting more like 4.6v from the arduino 5v pin.
If the 5V pin was reading 4.6V that could account for the inaccuracy. Why were you under that impression? Did you actually measure the voltage at the 5V pin? (You should.) How was the Arduino powered, exactly?
It seemed like using that external AREF trick was a good way to compensate for that. I suppose I should have factored out the switch to 3.3v to see if I got better results with only one change or the other.
If indeed there was less than 5V present on the 5V pin, then using the 3.3V provided by the onboard regulator was responsible for the increased accuracy. The change to the code is required to reflect the fact that AREF is connected to 3.3V, so just doing one or the other would have made things worse, not better.
But, if there is a power problem (5V pin not reading 5V) I'd give that priority and get that fixed. Connecting AREF to 3.3V was in this case fixing the symptom, not the underlying problem.
And the Pro Mini has no 3.3V regulator on board so that fix is not available as an option.