This would require spacetime to be quantized (presumably at the Planck length or something smaller) though, yes?

I've always thought entanglement makes more intuitive sense on a graph substrate of some kind, where the "spooky action at a distance" is actually just an anomalous edge in the graph connecting two vertices which would otherwise be more distantly separated. This begs the question of how the edges in the graph came to be or whether they're modifiable at all though.