Update in case anyone stumbles over here.
Twenty Eleven has a whole section called Responsive Structure which does what it sounds like it should do, but works counter to fixed layouts. The issue is discussed here:
By simply deleting the Responsive Structure section from the parent theme, all standard css properties work as expected, including no longer needing some kind of whacky background hack to connect the content to the footer. You lose a whole lot of smart degrading, I'm sure, but you regain the basics.
And, yes, I guess I did just edit the main Twenty Eleven parent theme, which esmi just told me not to do, and which I hadn't done up until now, but it seems unavoidable.