What about using some sort of air transportation? I seem to remember there is a helicopter that is based close to Negril. Fly from Negril to Kingston and then grab a cab for transportation around Kingston.
Actually a helicopter might be a little expensive, but a small prop plane isn't that expensive and you would have more time to sight see.
The Norman Manley International Airport is very close to Port Royal...
Negril.com - For the vacation that never ends!
These 2 web sites have small prop planes. https://www.timair.net/ and www.intlairlink.net
Did a search and came up with this:
https://us.jetcost.com/en/flights/ja...gril-kingston/
Recent flight searches Negril - Kingston
Flight Airline name Price Type Trip dates Search date Provider
Negril - Kingston Interisland Airways $116 Round-trip 31 to 31 August 144 days ago
Negril - Kingston Interisland Airways $56 One-way 07 August 193 days ago