After his band loses their only booking, a narcissistic musician goes back in time to steal hits before they’re famous. But when his scheme leads Kurt Cornell, his musical idol, to suicidal depression, he must overcome his own lust for fame in order to save Kurt’s life.

Not sure about narcissistic, as it is negative trait, maybe ambitious sounds little bit better? Names are also not important, just adds words into logline. Musical idol suffice, who knows, maybe producer would like to promote Justin Bieber lol.

What about:

While abusing his time travel ability to steal hits before they become famous, an ambitious musician cause suicidal tendencies in his idol and to safe him, he must overcome his own lust.

Its little cheese, but I cut down from 47 to 32 words.

I hope it helps! Its great premise!

btw, I love the premise, good luck with this!

In order to cut the word count I would get rid of the first line, "After his band loses their only booking,"
and start from that point.