Really bad idea!
FWIW, the PCB is already laid out fairly well. Power, ground and signal lines are travelling together from one section to the next, as they should be. Your suggestion would introduce large inductive loops in the ground return! 
Which is DC. Only ever a single transient when the latch is triggered. It is certainly the case that the 12 V should also be routed in proximity to the other lines but It seems rather improbable that this in itself would be the culprit. And note that the LEDs all have series resistors, damping any inductive transients. If anything, I would go with running sturdier wire on top of the ground tracks which clearly have been incorrectly specified and laid out - they should be at least four or five times as wide wherever possible (which considering the available board area, is everywhere 
).