The Bach quotes, and therefore had, the Megillas Taanis. He deals with the Beis Yosef’s (and Re’em, Me’iri and Maharal’s) Kasha, and doesn’t mention Chinuch as even a viable Terutz. (Perhaps he had the Bavli’s manuscript!)
So, if you want to mention the fact that the cleanup took eight days, as a Terutz, I can’t stop you. But don’t knock the whole premise of the Kasha by saying what the Gemara, Rishonim and Poskim don’t say.