On the question of Finn not following Rey in a skimmer, I couldn’t agree more with the desire to cut it entirely. The only question that immediately jumps to mind is some way to work in the story that’s told at the conclusion of the fight scene. Rey runs to steal Kylo’s Tie, and she flies away in a single panning shot that includes Finn and then the entrance of the Falcon to pick him up. The shot could be trimmed before Finn enters frame, but it’s sole value lies in Finn watching Rey leave, so they know they don’t need to pursue her/take them with her. At the very least, I think there’s value in simply using the shot of Finn in the death star interior and hearing the sounds of the saber fight, but cutting any subsequent interference with or even observing the fight itself until he pops into frame to watch Rey fly away. Of course, one might then desire some way of him knowing it was Rey who flew away in the Tie, unless that’s chalked up to his still budding force sensitivity. Ugh…what a mess.
All the other ideas you’re throwing around sound great, but I think Finn being there has a major purpose in the movie. Finn has been almost senselessly trusting and chasing Rey for 3 movies, and being thrown back by Rey is a turning point, where he realizes it isn’t his job to help her.
Even more so, Rey throwing Finn back is a sign of how desperate she is, how much she has (unwisely) taken all the responsibility on herself, and how close she is getting to the dark side, culminating in killing Ben.
Rey’s struggle is perhaps the clearest narrative thread, it’s worth enjoying!