>You can set the experiment up so the energy is the same in both cases (for example, both positions at the same height, just horizontally separated)
The action of placing them, say with your hands for simplicity, into different horizontal positions means differently pushing the Earth with your legs. For more cleaner illustration - let's say in our experiment a space ship is placed into orbit clockwise or anti clockwise. We can't just teleport the ship, so let's say we move it by rocket engines. So the ship goes in one direction, rocket engine exhaust goes in the other. The exhaust does have mass and speed. Even if it wouldn't eliminate the superposition gap, it will definitely decrease it, and decreasing the superposition gap increases the chances that some other unaccounted for factor(s) (for example gravitational waves caused by all these movements) will eliminate it or decrease further. Even if ultimately we still can't fully eliminate the gap, significantly decreasing it may eliminate various divergencies arising from quantization or make them very smallscale/localized (an observer from Alfa Centauri wouldn't care about the ship's orbit direction like we don't care about the spin of a given particle in the air around us) and average-able out on larger scales.
> The action of placing them, say with your hands for simplicity, into different horizontal positions means differently pushing the Earth with your legs.
This might change the momentum, but not the energy if the heights are the same. But if your point is that there will always be some difference in a conserved quantity, yes, that's a fair point.
But it also means that there will always be some difference in the spacetime geometry. None of the other factors you talk about would eliminate the "superposition gap", because none of them cancel out any changes in the spacetime geometry; they just add more changes to it.
> average-able out on larger scales
But if you don't have a theory that can represent the variations you're going to average out, you can't do the averaging. That's the problem: classical GR cannot represent "variation in spacetime geometry" at all. It can only represent one spacetime geometry. It can't represent a superposition of them, not even to do an average.
The action of placing them, say with your hands for simplicity, into different horizontal positions means differently pushing the Earth with your legs. For more cleaner illustration - let's say in our experiment a space ship is placed into orbit clockwise or anti clockwise. We can't just teleport the ship, so let's say we move it by rocket engines. So the ship goes in one direction, rocket engine exhaust goes in the other. The exhaust does have mass and speed. Even if it wouldn't eliminate the superposition gap, it will definitely decrease it, and decreasing the superposition gap increases the chances that some other unaccounted for factor(s) (for example gravitational waves caused by all these movements) will eliminate it or decrease further. Even if ultimately we still can't fully eliminate the gap, significantly decreasing it may eliminate various divergencies arising from quantization or make them very smallscale/localized (an observer from Alfa Centauri wouldn't care about the ship's orbit direction like we don't care about the spin of a given particle in the air around us) and average-able out on larger scales.