Well, as Alice would say, "curiouser and curiouser".
I took the board that has the most "bad" leds on it. Six, two on one side and four on the other.
I took a known good blue led from the baggie of leftovers, tested with a laboratory power supply.
I tacked it on to each bad led in turn. Four of six times not only did the tacked on led light, but the suspect one lit too!
Just to keep things more interesting, two out of the six bad leds did not light, but the tacked one did.
What the heck am I looking at here? Flakey solder joints that fix when I tack on a led and then fail again when I take it off? I tried reheating and adding a little more solder. Fail. Flakey outputs on the shift register chips or insufficient output loading?
Thanks for any and all suggestions.