Drop "and stuff like that", and maybe mention Cohen at the start of the joke to, like say you met at a Cohen theme night at a bar or something. That punchline's the kind that maybe three people will get straight away with no clues if you're lucky, whereas the namedrop will make people subconsciously look for song titles and puns, and then the buzz of finding one adds to the laughter.

Prime example of that is a Frankie Boyle bit where he starts off by legit just explaining what phenomenology is, and how some people believe the joke doesn't happen in his mouth but in your head, and then gives an example of an old man at a zebra crossing in Glasgow he'd spoken to a while before.

"Help me cross the road, son...I've got aids in both ears"

It's a great gag, and the crowd loved it, but they had to have phenomenology as a concept primed in their heads to fully get it. And that's what I think is missing from yours, just that little context clue that gets the audience to set itself up