I agree that "show more" is not the right form of interaction for a documentation page. Have you considered measuring engagement in other ways (tracking search results, link clicks, anchor clicks, short "is this page helpful" inline surveys, etc.)?
I do track the other interactions you mentioned, but it's difficult to map them to actionable ways to improve quality. And then even if we do make them actionable, it's hard to prove that they have actually improved quality. I'm just starting out a rigorous study of this field, though, and am hopeful that we can make advances.