Sully probably doesn't feel as hohum as you do about not being concerned about bird strikes. Go ahead and go to that heads down, who cares what is in front of the window approach. I was heads down getting LAX approach charts out flying a Cessna 340 over LGB when I noticed the lighting seemed different and I was nose to nose with a single engine aircraft. Not knowing which direction he was going to turn I rolled inverted because I had only one move. When he rolled right as he should have I paralleled his wings and rolled with him clearing by about 50 ft. No reports were filed but when he first saw me I was inverted. I wish I could hear his story because probably nobody would believe him. He did the right thing but I wasn't sure he would.
I instructed aerobatics so just pulled back enough to clear him after going inverted. I could pull away more than he could push over. Birds have to be seen to be avoided. Heads down means no bird avoidance so if you are flying into an airport like TGU you need to be heads up because they are in flocks and can easily be seen if you keep your eyes open, not down pushing buttons.