Does a physician's choice to opt for a less effective and less life-threatening treatment for a patient—instead of a more effective and more life-threatening one—constitute causing their death, thereby necessitating expiation for accidental killing, or is it a mistaken judgment that does not require expiation?

As long as the patient died from his illness and not from your treatment, there is no sin upon you and no liability; because you did not directly cause or contribute to his death. The most that can be said is that you did not take the correct path to save him, and this does not entail liability. The majority of scholars do not impose liability on one who intentionally neglects to save the life of an innocent person.