A battery pull isn't necessary; you can shut down the phone with a little practice (depending on your lockscreen).
1. Press the power button (or wait) to lock the phone
2. Press the power button again and unlock
3. [optional] Press the home button (center of screen near bottom edge)
4. Press and hold the power button until a short vibration is felt.
5. Touch the Power Off button (center of the screen just below a horizontal line from the midpoint of the volume rocker). This puts you in the Power Off confirmation dialog.
6. Touch the screen in the approximate location of the "OK" button. I start at the middle on the right side and work my way down. Soon I get the long vibration telling me the phone has powered off. This is the hardest to master since feedback isn't immediate; the long vibration happens several seconds after I successfully hit the OK button.
7. If nothing happens, press the power button to re-lock and start again.
8. Practice when the phone is functioning normally, and you'll be prepared for your next SOD.
My observations (bone stock GSM phone):
This happened once in a pitch-black room. The screen does not go perfectly dark, but it is extremely dim and uniformly grey. I could not make out any details, so the contrast is completely gone.
SOD happens all the time playing Ingress, or other apps where the screen is active for a long time. It seems to happen most often when the display partly dims before going to sleep. My phone is set to sleep at 30 seconds, and the "pre-dim" happens at about 25 seconds. That's usually where I get my SODs.
SOD happens to me less often with auto-brightness set to OFF. It's extremely rare in normal use (but happened just now as I replied to a text!)