First of all, your assumption is wrong.
Harry never taught DA the "Levicororpus" spell in OoTP book (confirmed by searching ebook text) - that event only happened in the movie/game based on the book, which are not canon.
Second, the spell was actually introduced much earlier than HBP, although not named:
in OoTP when Harry saw Snape's memory in the Pensieve of James Potter using the spell on Snape during their time in Hogwarts.
... James whirled about: a second flash of light later, Snape was hanging upside-down in the air, his robes falling over his
head to reveal skinny, pallid legs and a pair of graying underpants.
As a matter of fact, the spell was first introduced (but not named) in HP4, GoF; as we see in HBP recollection:
Hermione: "We've seen a whole bunch of people use it, in case you've forgotten. Dangling people in the air. Making them float along, asleep, helpless." Harry stared at her. With a sinking feeling, he too remembered the behaviour of the Death Eaters at the Quidditch World Cup.
So yes, apparently "they" "did think this through", as you put it.