Okay, so some numbers, and perhaps (?) even a bad power supply.
I decided to do a comparison between the EX330, the MN35, and for a couple of the measurements a cheap multimeter that came in an experiment kit from a workshop.
Battery 1: EX330 9.29v, MN35 9.35v
Battery 2: EX330 9.26v, MN35 9.32v
Three batteries in series: EX330 27.82v, MN35 28.1v, cheap DMM 27.9v
Korad power supply running at 5 amps into a bulb, measured at bulb terminals: EX330 13.19v, MN35 13.28v, Korad display 13.30v, cheap DMM 13.25v
So at 9v the difference between EX330 and MN35 is 0.06v, at 13v the difference is 0.09v, and at 27v the difference is 0.3v. If that tells you anything. (Not quite linear with voltage.)
I also measured the AC component of the power supply output with a scope while the power supply was driving a bulb at 5 amps. I noticed that if I dropped the voltage below 7v (under load), with the next relay click I saw a huge jump in running noise on the scope, going from less than 10mv peak to peak up to 125mv peak to peak. I can take some screenshots and/or measure it if that is of interest (or maybe I start a different thread on the power supply). I checked this to see if maybe an AC component on the PS output would be causing a difference between the cheaper and the more expensive Extech meters.