> For example, if “space was expanding” except for things that are close enough overpower it with gravity, how would that result be different from dark energy creating a repulsive force except for things that are close enough to overpower it with gravity?

The main problem is that dark energy's repulsion has no intrinsic link to the global expansion of the universe. For example, as I noted in another comment, in Einstein's static universe (in which matter's attraction balances dark energy's repulsion), there is a repulsive force even though the universe is not expanding.

More generally, the repulsion from dark energy has no link to the cosmic expansion rate at a given instant. It does connect to the rate of change of the cosmic expansion rate (i.e. the acceleration), but this link is only partial, since dark energy is only one of the factors controlling the rate of cosmic acceleration (the other main one being matter, which decelerates expansion).

> Also, how can galaxies be “carried by their initial momentum” as you confirmed above AND all be moving away from one another at the same time. Maybe I’m misunderstanding something but that doesn’t really make sense. The only way all galaxies that are not locally bound to one another could be moving away from one another is if that space between them is somehow expanding, similar to the “dots on the surface of a balloon” metaphor that is often used. If we instead imagine an “initial momentum” scenario, it suggests a single point of origin in space, similar to an explosion. But in the case of an explosion, there is a center source, which the universe doesn’t appear to have.

The universe can originate from a single point in spacetime while still having no center in space. Due to the principle of relativity, any observer departing from that point has an equally good reference frame, so there is no way to decide that one observer is better than another.

(You could still suggest defining the center in terms of "distance from the edge". There doesn't have to be an edge, though.)

> Also, the red-shifting caused by an explosion would not be so uniform, but have many items moving away at much faster speeds than others relative to the observer.

That's not a fundamental limitation, it's just intuition from the explosions you know. The initial "explosion" doesn't have to be messy (for example if it arose from inflation). Also note that in an expanding system, velocities self-sort because if an object is moving rapidly with respect to the material near it, it's not going to stay near that material. Instead it will gradually end up near material moving at the same speed. (This effect is essentially the cosmological redshift applied to massive particles.)