@penguin: I see your point, and I also like your suggestions for "Schulmedizin".
And you might also be right about how the main difference nowadays is not so much the fact that one group has studied medicine at an university and the other group has not (given the fact that alternative approaches are increasingly being taught at universities as well).
Nevertheless, I think that in general, however, "Schulmedizin" still refers to well-established medical theories and practices that are passed on in institutionalized, academic settings as opposed to alternative methods and approaches that are traditionally passed on much more informally form one practitioner to the other.
See the respective entries for "Schulmedizin" in Duden or DWDS, where S. is referred to as "[den] allgemein anerkannte[n], an den Hochschulen gelehrte Lehren und Praktiken der Heilkunde" (see DWDS) or "[der] Medizin, die an den Hochschulen gelehrt wird und allgemein anerkannt ist".
So in conclusion, I think conventionally trained physician might be a good solution then. I even found a few instances of that on the web.