I think the doctor should be proactive and try to educate his patient. He could inform them that in every drop of breast milk there's 1 million white blood cells, so if God really said not to eat blood the way the WT says then why is there blood in the milk. And if your to pour out your blood again like the WT says then why do they allow blood fractions which are obtained from donated blood. These are questions and comments that may get a JW thinking, and the doctor could finish off by saying "are you really sure your leader's are correct on this matter so much so that your willing to die? Because in 1967 they told their followers not to have organ transplants even if it meant death, then 13 years later they changed their minds"
As the doctor I would hope this would get the patient thinking and then do to the pressure of imminent death maybe change their minds after planting these doubts.