Hey @patrick_at_nebraska_medicine,
Definitely sounds like a challenging situation, especially since Google can run things on their own terms sometimes. I would definitely recommend checking out @HeatherPhysioc's Moz article on SEO Maturity: https://moz.com/blog/seo-client-maturity
I connected with @zac_heinrichs from our team at Moz and he agreed that you are likely on the right track with search intent. If Google believed that they could make money by showing ads for "kidney transplant", they would -- but since that is such a top of funnel keyword, they are likely displaying more informative resources, rather than a "book your appointment" type of search result. This is where your idea on more general content could come into play. Articles that answer questions like "what is a kidney transplant?", or "how does a kidney transplant work?" could work well here.
When I worked closely with agencies here at Moz, and I found that the best way to get buy in from customers is to show how the efforts are impacting the bottom line - telling the story about how more conversion oriented ads are leading to more bookings and ultimately more revenue for the client. It's likely that an ad for something top of funnel like "kidney transplant" is not converting as well and its not because the ad isn't appearing, it's because those people are not looking to book an appointment at that time.
Definitely looking forward to hearing more about what happens with your client and wishing you all the best!