Could Nelson and Rodney have traded their 6-inch secondary battery for more shafts and speed?
Short answerPossibly enough for a third shaft, but probably not four; the Royal Navy retained a battleship secondary battery because the ships were treaty replacements for battleships.
NotesThe Nelson class carried a battleship-scale 6-inch secondary battery because the two ships were replacing battleships under the treaty. Reducing that battery could free weight for machinery. The saving might have supported a third shaft, though probably not the much larger change required for four shafts and their associated plant. The choice therefore linked tactical identity to propulsion: treating the ships as battleships protected their secondary armament at the expense of possible speed. Several individually sensible requirements could close off a faster overall design.