Sure, you can find private operators who will go there. Those allowed inside the compound at the pier are supposedly 'approved', as opposed to those outside the gate.
I have to admit that I am not a fan of Jamaica although I know people who live there, both in Ocho Rios and Falmouth. I became friends with a bartender on the Liberty Of The Seas recently and he lives in Falmouth. A long-time acquaintance owns condos in Ocho.