I very much like that you are a string theory researcher who is willing to look at discrete models and I like that you are thinking in terms of a many-worlds interpretation and ER=EPR. I also like that you are thinking in terms of deterministic, not observer dependent many-world states.

The Penrose Interpretation has been related to ER=EPR and I think something like this could be used for choosing one of many branches for the many-worlds out of a superposition. I tend to think you are going to need a superposition of states, even a superposition of universe states with ER=EPR-like connections. The choosing of one-branch could be some kind of Penrose interpretation limit causing the loss of ER=EPR-like connections between worldlines/universe states.

I also like your idea of interpreting particles as higher dimension structures. I tend to think of the higher dimensional structures as information on the vertices with gravity CA on the links but really at each vertex at low energy there would be a structure to think about for the higher dimensions also.

If that emergent graph with a single rule idea doesn't work out, perhaps you could look at something like U(N) gauge theory on D-branes but with something like an E8 lattice for the discrete D-brane. For this I tend to think that the different branches at a vertex would be represented by different rules.