If the cost to Baron to publish the letters is X, and the blackmail payment is Y, precommit to reject any offers with probability greater than 1-(x/y). That shifts Baron's expected value to negative (unless x=0), and increases the expected value for Countess by less than (1-(x/y))*(z-y), where z is the loss of value to Countess of having the letters published.

That strategy deters every Baron who is sophisticated enough to be deterred by a full precommittment, and does better against Barons who proceed regardless.