So to answer my own question...
In case anyone else is in the same boat:
There wasn't any location where I needed to apply pressure. The reason that the simple screwdriver-in-center-hole turn didn't work is that the deadbolt was stuck in the strike plate. The amount of force needed to overcome the stickiness of the deadbolt was more than what the turning mechanism could support with a screwdriver.
So the only way I was going to be able to get the deadbolt to move is to pull it directly back.
Although I ended up crushing and bending the deadbolt assembly, I wasn't able to open the deadbolt until I could actually grab the top of the bolt and pull it directly perpendicular away from the strike.
What I realized afterwards is that I might have been able to pull the little tab with needle-nosed pliers. I circled the tab in green and showed the direction to pull with the arrow.
So if you find yourself in a similar situation, try it first.