What if, instead of deciding whether the doctor murders the patient in secret when she comes to the hospital, we have to decide whether the government (perhaps armed with genetic screening results seized from a police databases and companies like 23andMe) passes a law allowing police to openly kill and confiscate organs from anyone whose organs could presumably save five or more transplant patients?

As far as I can tell, this would have no bad effects beyond the obvious one of killing the people involved - it wouldn't make people less likely to go to hospitals or anything - but it keeps most of the creepiness of the original. Which makes me think although everything you say in this post is both true and important (and I've upvoted it) it doesn't get to the heart of why most people are creeped out by the transplant example.