Looks like it was just an audio power issue. I was testing the single-shot mode using an old cassette-type walkman, and the machine-gun mode from the audio of my smartphone. I have a speaker to monitor the gun sound, and it was obviously must quieter on the smart phone. So I made a tape of the machine-gun sound, and things seemed to work right. Here's a brief video showing the result:
http://www.bowersflybaby.com/gunvideo2.wmv
Note that the rhythm of the gun is a bit uneven (I just strung together duplicates of one Mosin-Nagant shot) but the high-powered LED is tracking it pretty well.
I want to fiddle with the circuit a bit, but otherwise, I'll be posting a schematic in a couple of days.
Ron Wanttaja