How about tip125 as the anode-side switches? They have max current of 5A and current gain of 1000. So for a 1.2A collector/emitter current, the base current would need to be 1.2mA. A base resistor of 2K2 would give a base current of 2.3mA, more than enough to saturate it. As it would be driving the common anode layers, one at a time, a 74hc595's current sourcing abilities would not be an issue.