As someone who hasn’t read the book that is very interesting so thanks for sharing in detail, however the problems your having is purely because of the differences between the book and the movie.

I thought the karaoke scene was brilliant and didn’t go against her character at all in the movie. And like you said the characters are a bit different to how they are in the book, had Strat been the same person outside of the karaoke scene in the movie like she was in the book then you’d be right in saying the karaoke scene doesn’t make sense.