On the main topic of believing in Gemorah medicine. I am not going to hunt for quotes, but I would think that Rambam himself demonstrates same attitude that his son is referring to. He is clearly using science of his time. Also, Gemora itself describes multiple cases of Amoraim knowing or not knowing various medical facts and relying on factual proofs to make decisions. Just study Shmuel’s approach and try to describe how he would behave in our times. I think he would go to medical school.
Also, just a simple observation that amoraim argue with each other on all kind of points makes it clear that none of them has access to the absolute truth on anything. Their overall approach to the argument is such that they are able to develop a coherent system of making decisions. And even then, they leave multiple questions without a clear answer or to defer to Eliahu. This is indisputable and should be a starting point for any logical argument on the topic.