Those puppies are really bright! And I'm sure folks took advantage of that light source back in the day.
One very important point missing from the previous discussions is that all batteries have an equivalent internal series resistance. It's roughly based on the chemistry and the physical size of the plates. But in general a lower AH capacity battery would have more internal resistance than a larger one of the same construction. It's this internal resistance that is the real reason your voltage was pulling down more so when you tried the smaller AH capacity batteries. Based on ohms law(V/I=R) if your battery voltage was being pulled down 1.5 volts under load, you'd divide 1.5 volts by 3 amps, which gives an equivalent internal series resistance of .5 ohms. If you pull even more amps through that same .5 ohms then you'll have a proportionally larger internal voltage drop. Hope that all makes sense.