How Do You Follow Parody?

I very lately watched The Hunger Games for the first time. I have never read the book, so my comments are limited to the movie.
Early in The Hunger Games, Katniss parodies the Hunger Games' official language by mocking, "May the odds be ever in your favor." (Parenthetically, I'm a little weirded out by the way American movies sometimes use English accents and Anglophilia to make characters seem villainous. But that's beside the point.) The interesting thing is that we, the audience, get this parodic treatment before we ever hear the Games officials using that phrase. When we hear the phrase for the first time, not only are we primed to think that it is a mark of oppression, but we are also aware that the characters are willing to undermine their authority (in the safety of remote hills).
This scene reminds me of a passage in Stephen Greenblatt's "Invisible Bullets," which draws connections between Shakespeare's Henry IV (1 & 2) and V and Thomas Harriot's account of English colonization in America. Greenblatt describes how Falstaff's antics parody King Henry IV's rhetoric before the king speaks. Falstaff announces that he is called about at all hours because he is an important man (when it is really because he is a scoundrel); in the next scene, the king is struck with insomnia and laments that great men cannot sleep while small men slumber. Greenblatt writes, "As so often, Falstaff parodies this ideology, or rather--and more significantly--presents it as humbug before it makes its appearance as official truth." The results are perhaps subtler in 2 Henry IV than in The Hunger Games: "Its effect is not (as with more straightforward parodies) to ridicule the claims of high seriousness but rather to mark them as slightly suspect and to encourage guarded skepticism." As a result, the king's rhetoric "reverberates hollowness as well as poignancy." I would say that in The Hunger Games the result is of the more straightforward variety.
In either case, it seems that what Greenblatt calls anticipatory parody is more effective than reactive parody. For those of us who are parodists, that's something to keep in mind. But in thinking about this I have a further question: what do you do when your own project or rhetoric has been parodied in anticipation? How do you speak when your speech has already been mocked? How do you follow an act that already undermines your own?