I see what you’re going for. Personally, though, I think the information that Poe delivers to Finn about BB-8 and his mission on the TIE fighter, which he then passes on to Rey, is more important for the audience to know than it is to address though issues, which are relatively minor to me.
Maybe I’m interpreting it wrong but it sounds like from this restructure the audience might learn that during Poe’s interrogation, but Finn and Rey don’t. But they need to know he is important in order to encourage Rey to go on this journey.
And I also think it might be just as unclear for the audience how he was rescued from the Star Destroyer so quick and immediately jumped into the battle, if not moreso than the explanation he gives in the movie.