The correct answer is D) changing the setting of the tappet collars on the pilot valve operating rod. The total length of stroke in a reciprocating steam pump can be adjusted by changing the setting of the tappet collars on the pilot valve operating rod. This allows the pilot valve to open and close at different points in the piston's travel, which in turn adjusts the stroke length. The other options are incorrect because: A) twisting the stay rod would not affect the stroke length, B) variations in the throttle adjustment control the steam flow but not the stroke length, and C) changing the number of packing rings around the piston rod would affect the pump's efficiency but not the stroke length.