It all kind of makes sense at the time, but recapping old adventures inevitably results in them sounding like zany antics. So make sure you provide opportunities for characters to do this, and try to explain all the weird stuff they did. Preferably to serious people like the King or the High Wizard of the Realm or something.
Commentary by memnarch (who has not seen the movie)
Excellent recap of your adventure so far Finn; I trust there's a point to all of this?
Perhaps Finn is soliciting feedback on whether he should try and kill Poe or try to stay friends with Poe. Annie did say to the GM waaaaaay back at the beginning that "it's going to be tough for them to trust you." We've had more than a few instances of the other players not having trust in Finn/Annie so far, but could whatever this thing might be still be something in motion? The whole Anakin thing took way more than a single movie after all...
Finn: I swore whoever killed Gil would pay in blood. My commanding officer wouldn’t let me search for the killer.
Finn: I pretended to seek an undercover job in the Resistance so I could be free to hunt them down.
Finn: The First Order partnered me with Poe. I learnt he killed Gil, but then a minute later our ship crashed and he died.
Finn: Then later his twin brother Allan appeared. We got into some tough adventures, but saved the Resistance.
DJ: Wow! I bet he did all the good stuff!
Finn: We became friends. He was a good bloke. But then he got killed in a hangar explosion. And their third twin brother Edgar appeared.
Finn: But it turned out it wasn’t really Edgar, it was Allan pretending to be his own triplet.
Finn: So now I was incredibly relieved that Allan was still alive. I hadn’t lost another good friend at all.
Finn: And then it turned out that wasn’t really Allan, but Poe, who’d survived the crash and pretended to be his own twin to throw off suspicion of being a double agent.
DJ: Vir summo ingenio! This sounds like a fantastically clever plan!
BB-8: It had my head spinning a few times. It didn’t used to do that.