Not sure that this is right:
As you walk the pack moves from one side to the other. A rigid load moves from left to right all at the same time. But the water in a bottle moves slightly slower, so that the swing of the pack is reduced
The swing of the pack is the same - the torso and the pack affixed to it describes the same lateral arc away from the midline. What you might be describing is a phenomenon where there is latency in the water moving away from the midline to the extremity of the arc - because it is a fluid. Assuming that the torso swings in the same arc from left to right the water may tend to 'peak' in the midline but this would only be a portion of the fluid and it doesn't mean that the walker uses any less energy to walk up and down hills but it might mean that the walker uses less energy to move the torso from left to right. remember that in level walking oscillation of the torso away from the midline is minimal so any energy saved by postural muscles is likely to be similarly minimal. There is movement in two other planes but the principle is the same even if the movement of fluid id highly variable.
However, when the walker negotiates obstacles and leans the torso over to one side (i.e. crossing a log, scrambling on rocks) that water will tend to spill over to whichever side that the walker is leaning towards, increasing the energy required to get that water back to the midline (I forget the physical principle but the mass at the end of an arc requires more energy to return to the midline than if the weight were closer). This is really noticeable when you are carrying a lot of water in one container. This property of the fluid might well might negate any advantage that was described above.
I am not sure that there is any effective energy return in the system - what you seem to be describing in your discussion on springs is a kind of sloshing backwards of water helping to bring the torso back to the midline and increasing efficiency of the postural muscles. This is plausible but in reality would require harmonics - the net direction of flow of the water in the vessel corresponding exactly with the movement of the torso. This system still requires enrgy to move the water from side to side unless you are proposing a perpetual motion machine....
In reality what i have noticed is that, when carrying a large water vessel (the 25l jerry on my back), the flow of the water might be in the opposite direction of my torso - so that you are 'fighting' the weight of the water that is moving independently of the torso. Runners who carry water really notice this effect and try and reduce sloshing as much as possible by placing baffles in their water containers.
I am not sure that an experiment would be of much benefit because, as you state, perceiving any energy gain or loss using your perception is pretty flawed. You could do a controlled experiment in a physiology lab to measure energy consumption but you would need a number of repeats, a number of controls etc to do it properly.
Fluid dynamics is really, really complicated maths and I don't pretend to have a grasp on it but I think that carrying bottles in the midline and minimising slosh is the most efficient method based upon my limited understanding. I try to carry water bottles on my shoulder straps with my spare 2L in my pack at my midline.