Correct me if I am wrong Dave- but wasn't Rodney with the HF at that time-given that she was the BB count would have been two 9 X 16" gun BB's and one 14" BB- ranged against the major KM units Bismarck,Tirpitz and Scharnhorst????
Rodney was already on its way for an extended dock yard stay in late May when it was historically diverted to the Bismarck hunt. It would likely not be available for the hypothetical time period.
The British really needed new battleships to counter relatively new battleships deployed by the enemy. It has been pointed out by Admiral Mustin, that the North Carolinas were: "an order of magnitude more capable, even with modernization, than the old battleships." Deploying modernized but old battle cruisers to combat was a mistake made by the Japanese.
The same applied to KGVs vs old British battleships. The old British battleships with the exception of Nelson and Rodney, even with added armour during modernization, had weaker protection than the Hood had at Denmark St.
Although, Rodney had 6" deck protection over the magazines, over the machinery it was only 3". But it was really such things as firecontrol where old battleships were most wanting.