I thank the readers who suggested publications that might include the concept I blogged about a few days ago, the extent to which IV estimation diminishes precision (power) relative to a straight-up RCT estimate.
Though it is possible some of that literature implied the result Steve had obtained, most of it seemed either not quite on target or more complex than necessary. So, I took the trouble of
writing up the proof more carefully (PDF) and confirming it for myself writing it up and subsequently refining it (see update in a later post).
I still think this must be a known result, and if you are aware of a publication that includes a proof in a simple form, please let me know.