If the pool is the only reason you want to switch and you figure you'll be miserable without it ... then book at CocoLaPalm, for the 6 remaining nights.
Spend the night you paid for at BBB and then move.
But i stay in a place that doesnt have a pool and it works out okay for me.
You can swim in pool in any city, enjoy the sea when you're in Negril! -- thats how i look at it anyhow