I have to agree that the West end is a lot quieter at night.
You could go with Marko's suggestion: Enjoy the beach during the day and sleep on the cliffs at night.

If you would really prefer to be on the beach end of Negril, then I would recommend the other side of the street. I stayed on the Gardenside on my first trip to The Grand Pineapple and it was incredibly quiet at night. You only heard the tree frogs.