I figured out a solution!
First, I thought that maybe -- who knows -- that adding in "font-size:0" might do something. Well,
rather interestingly, what that accomplished was to actually create
negative line height, i.e. not only was that line not hidden, but instead it
decreased the space between the poem and the paragraph before it! I can't imagine why, but that's what it accomplished.
So then -- for lack of anything else to do -- I changed that to "font-size:1" (without specifying what "1" was measured in, i.e. em or px or whatever), and although that seemed to do the trick for ADE, I was back to where I was before with iBooks (with an extra blank line added).
So then I changed that to "font-size:1px", and that seems to have done the trick! Seems to work out just fine in both ADE and iBooks, and if there's a 1px line added in there, I can't really see it at all.
So I guess I solved this -- but thank you for pointing me in the right direction, of course! I guess I should really say that "we" solved this, together.