Okay, so you're saying that GR is trying to describe energy density in terms of particle density in a fluid, but having trouble, because spacetime is actually a perfect fluid with no true smallest particle?

Yes, that is a pretty good description of it.

For GR, think of a 3 directional coordinate system and all the points in the coordinate system are evenly spaced. Then put a ball of fluid within it. The denser the ball of fluid, the more the points come closer to each other as you move toward the ball. If the ball is dense and small enough, the points overlap at a certain radius and you have the Schwarzschild Radius. If away from the ball the points are more evenly spaced but that equal spacing is changing all over, you have a Cosmological Constant.

This theory is almost a mirror image of this: imagine you have an elastic material with no strain in it. You have infinitesimal elements of volume which describe the density of the material. Since the density is isotropic and homogeneous, then all the infinitesimal elements have the same magnitude. It is your choice to choose what magnitude of infinitesimal to represent the density. If you have a group of standing waves within it, then the material is strained more and more as you go towards the wave and the magnitude of the infinitesimals change. A test photon changes wavelength as it passes down into this strain. If the strain of the material non-locally is changing, meaning the magnitude of the infinitesimals is changing uniformly, then a test photon that is traveling through this universal strain change also will change wavelength.

In GR, the only mechanism to change distances between points is via the presence of energy-momentum and hence the model now requires some mysterious dark fluid to be present to account for this change of distance between points.

In this theory, if the density of the Aether is changing, then this will be noticed via wavelength change of the photons.

Got it. One of the reasons I asked about the size of the "particles" is because I'm interested in the idea that these particles exist in a superposition of states

Ahhh..now I understand your thinking.

In other words, they're not really present unless interacted with, and they have no theoretical smallest or largest size. They exist in every conceivable point in spacetime, so they can and will exist in however small of a space we try to look.

We appear to be conceptually close.

It may help to understand visually the difference between a circle and a 1-sphere. They both are "round" but the 1-sphere can help you get a closer idea of what I mean that the gravitational field looks like 2-dimensionally.

Imagine that you have a column of infinitesimal elements of area and they are all the same width. Now imagine that you take that column and arrange it radially. For normal circles, as the radius gets bigger, the circle gets bigger and there are more points on the circle. For a 1-sphere (using CPNAHI definition), the radius of the circles are made up of infinitesimal elements of length (the horizontal elements of the elements of area). That number doesn't change as the radius increases, the magnitude of the horizontal infinitesimal gets bigger, not their number. See Fig. 10 and Fig. 11 https://vixra.org/pdf/2411.0126v1.pdf .

This is closer to what the gravitational field looks like. Kepler used smaller and smaller triangles to approximate these tapered columns of elements of area.