I would think a spade bit would give you the counter bore for the screw head and washer you're talking about. But I would be wary of the rest of the plaster just disintegrating and falling down anyway.
True, just thought a cleaner hole would give less chance of a stress riser. But then, that is total guess work and only what I would do if tackling the same thing myself. DO NOT TAKE MY ADVICE!!!
I would think a spade bit would give you the counter bore for the screw head and washer you're talking about. But I would be wary of the rest of the plaster just disintegrating and falling down anyway.