I called San Jun hospital to ask to speak to the above-mentioned psychiatrist, Dr. Wan4 Fang1rong2, about mental health care for foreigners in Taiwan, and mentioned the assembly-line concern. He agreed, that's pretty much the rule here, although he confirmed what I had heard about him, that he himself takes more time to talk. But in order to do that, he accepts only a smaller number of patients. There's the rub.
I asked whether there was anyone in Gaoxiong he could recommend for you, and he mentioned that if you go to the Veterans' General in Gaoxiong and ask for Dr. Lu4 Ti, 陸悌, and tell him that Dr. Wan Fangrong of Taipei recommended him as someone who would be willing to take more time to talk to you and help you personally, than Dr. Lu will probably squeeze in more time for you if at all possible -- but no guarantees, because if his hospital has scheduled 200 patients for him to see in 2 hours, his hands are tied -- better 1 minute each than to leave some of them without pills.