How about - instead of tying OE to ground, connect it to an IO pin (any free Arduino pin) and a 10K pullup resistor. The pullup resistor will keep OE high until you're ready for it, and when OE is high on a 74hc595 its output pins are in high impedance (disconnected).When your startup & config code is done running in your Arduino sketch, do digitalWrite(yourPin, LOW) to enable the 74hc595's output pins, and away you go.Good luck!
You can do that? That is beautiful.
shut off OE, update the shift registers and switch to the next row, then turn OE back on.