Spent the last 3 days reading this whole thing
So I think we've figured out who K was... (Josh). The only thing that's really confusing is the timeline. Are we sure "For K" is a real, official title? Could it be he just liked the song (which I'm almost certain is about a movie) and she dedicated it to him? I think the same about Jump and Mike Mizrahi. The Chet Baker theory seems too believable for that song to be about MM.