Thanks for all the tips. In the end, I moved everything one-by-one, didn’t want to sacrifice quality over convenience. It was a massive comp with precomps, next time I should plan things a bit better!
I wasn’t satisfied with how things looked. I need to change keyframes of multiple cameras, make things move faster etc. It would be very useful if I could just extract parts of the time line, so I don’t have to deal with layer keyframes later on the timeline.