Now I'm curious... Is your last suggestion correct? Wouldn't the time to cool down between pause intervals be proportionally longer due to the higher thermal mass and cancel out any savings gained by the long pause? Maybe the overall energy draw is even higher because the heat losses are higher when you spend a longer time with a high dT.
The water bottles don't warm up as quick as the air they replace that flows out of the fridge when you open it; so they have two effects first they take up space that new hot indoor air can't move into and second they then help chill that air slightly through their own thermal mass.
