Since I want to make it fully modular I need to have each PCB (pixel) both send its state to all eight neighbors as well as receive the neighbors states.

I gave this problem statement, together with a strict rule of  "don't cross the streams (wires)", to my wife and she came up with something looking like this:

Not bad at all actually.  But after looking at it for a while I realized it could be improved slightly by removing a redundant connection in the pass-troughs.

This could also be slightly improved by switching the horizontal interconnects to reduce the trace length on the PCB a bit.

I also need to add PWR and GND between all PCBs, but there's enough space for that at the left/right edge.