Okay. I ran the mod all day today, and it finally stopped firing. Results: battery in left hand slot = 3.20v, battery in right hand slot = 3.18. So that would be 6.38 total voltage. I've been changing them when I have one "bar" left on the gauges, and they come out about 3.5-something volts. I will continue that practice, as I like my batteries to be as stress free as possible.
edit: Btw, for clarification, I was incorrect in my previous post. The battery gauges were not showing empty when I changed the cells the last time. They had one flashing bar left. For some reason in my mind I was thinking that since my last bar was flashing I was out of power, but the mod will actually go down to no bars for a short time before finally shutting off. Sorry about that.