I think it’d be pretty easy to establish Rey in TLJ. A custom crawl explains the Republic has brought peace to the galaxy, but cannot crush the last remains of the Empire on Starkiller Base. Then the finale from TFA plays - Han is killed early on, Rey holds her own against Kylo, but Poe fails to destroy the base in time. It fires and destroys Coruscant.
Rey reaches Ach-To within the first 15 minutes. With the Republic gone the mission of Leia’s Battalion is simple - escape. And they are banking on Luke to save the day.
Finn can stay unconscious throughout. He is not needed because without TFA he won’t be an established character yet, and can easily be pushed to the sidelines. Instead we’d follow Rey and Poe.
Poe’s plan would be mutiny the Raddus, then attack the Supremacy dead on in hopes of temporarily disabling the engines and escaping. It’s dangerous but the only option he can think of. Instead of Holdo and Leia keeping the plan a secret, I’d change it to a public plan centered around Luke. Throughout the movie Leia will have faith that her brother will return, until she finally gives up on Crait - just as the Last Jedi answers the call.
However, while this might sound like a tighter TLJ, I’d actually advise against this. I think TFA is enjoyable and not worth cutting out. Rey’s character origin is a small price to pay for a good Star War Episode.