Substantivalism and locality

I find myself going back and forth between substantivalism and relationalism about spacetime. On a substantivalist theory, the points of spacetime are real.

But here is a problem. It seems essential to the concept of a point that geometric relations between points are essential to them. If two points are a certain distance apart, say, then they couldn’t be a different distance apart. But on General Relativity, where geometric properties are determined by the distribution of mass-energy in the universe, if geometric relations between points are essential to them, locality is violated. For imagine two events that are distantly spacelike separated. Then the geometric relation between the points at which the events are found depends on the distribution of mass-energy between the events. If the geometric properties are essential to the points, then influencing the mass-energy between the events will affect which points these events happen at. And that will be a non-local influence.

Perhaps we can say that only local geometric relations are essential to points. Perhaps the way to say this is that if a point x exists in worlds w₁ and w₂, then there is a set N of points such that every member of N exists in both worlds, and N is a neighborhood of x in both worlds, and the geometry on N is the same in both worlds.