But I struggle to see what evidence could neatly distinguish between these cases. If you have an idea, I'd be keen to hear it. :)

I'm not sure there's much of a difference between the "doctors care about healing, but run into imperfection and seflishness" interpretation and the "doctors optimize for signalling, but that requires some healing as a side effect" interpretation besides which piece goes before the 'but' and which piece goes after.

The main difference I do see is that if 'selfishness' means 'status' then we might see different defection than if 'selfishness' means 'greed.' I'm not sure there's enough difference between them for a clear comparison to be made, though. Greedy doctors will push for patients to do costly but unnecessary procedures, but status-seeking doctors will also push for patients to do costly but unnecessary procedures because it makes them seem more important and necessary.