There are two elements that feature here:
1. Editor/Editor Settings/Editor Help Display
This one I have doing exactly what I want - it's set to Focus, so that if I want to read the tooltip, I can click on it. This is incredibly useful and thoughtfully designed. I mention this first because I thought it would solve my problem...but it doesn't.
2. The hover tooltip - this feature, in the Editor itself (not in-game), I cannot seem to disable and would like help removing it. Is it possible to disable the hover tooltip in Editor Settings?