>A good start, but shopping around is hard, if not impossible

I think shopping around, properly conceived, should be the primary care physician's job. If a doctor is referring e.g. 10 people a month to a specialist, then obviously they are going to be in a much better position to evaluate the options than a patient.

I believe that Sherpaa, Jay Parkinson's company, provides this "shopping around" service (https://sherpaa.com/).