I don't see how that is possible. The power and signal of the arrays share a common ground. Meter the resistance between the two grounds on the board, and you will see. And you should run signal wires alongside a ground anyway, to mitigate RFI and maintain a reasonable impedance. Also, your 12AWG wires are wasted if they only interconnect the arrays in a chain. You should run them as a bus, and tap power from it for each array. Unless, there are some very heavy PCB traces for power and ground on the boards.
This is more of a physical question, so you need to post some information about the actual displays and wiring, not just diagrams.