To answer your questions below:
I know other non resident, non citizens who have brought TV's down and not paid duty on them. I don't have a code section to refer you to to confirm this, but it applied to me and I paid no duty on my carried on TV in its original box. The values assigned to my goods were done by the customs officer. I've had people say that most barrels are valued at an amount that will create $5,000J of duties unless they are clearly more valuable items in your barrel.
You have to deal with customs directly at the Wharf. I've been told that you can use a customs broker to handle that for you, but I have no first hand knowledge of the cost of their services. I beleieve they are set up for commercial activities, not personal stuff.
I highly recommend that you use a qualified Jamaican resident to clear the items for you. In my case, we labelled the barrels with my name and/or my Jamaican friends name. Make sure your name is the exact same as on your passport/TRN. Do not use nicknames. I had to pay $600J to have my documents amended for Tom vs Thomas.