I turned off all extensions and, while it didn't make any difference, I noticed for the first time that the behavior only occurs when I'm at the top of the page. For example, if the page begins:
====== H1 Title ======
===== H2 First Subheading =====
Blah blah blah...
then, when rendered, the extended menu displaces the text under the First Subheading (it causes the text to be reflowed so as not to be overlaid by the menu). But if I scroll down just enough that the Title scrolls offscreen, the extended menu always overlays whatever's there, which is what I want.
I tried removing one pair of '=' signs from the H1 Title to see if the problem was related to H1, but I still saw the same behavior. I tried putting some text both above and below the first header: the bad behavior ends as soon as the first header has scrolled out of sight.