Time flies, but I finally took my distributor apart yesterday. Contrary to what the Haynes manual says, and my memory was correct, the pick-up/trigger isn't movable.
The pick-up actually has an inner and outer bit (photo below), so I suspect it doesn't matter where exactly the magnets fly through.
So, I'm a bit stumped. Winter has worsened this problem again, driving the first mile on three cylinders.