Lola brings up some interesting information, but I am not sure how really useful it is for most visitors to Jamaica.
The situation she is talking about, especially for Jamaican women, refers to residents (person living in the area) choosing which taxi to take. These people LIVE in the area and have thousands of daily experiences with drivers. They have their favorite drivers that they regularly use. They have drivers that they do not like and will not get in their vehicles. Visitors to the island do not fall into this category, as they dont live here and they dont have years of daily experience with the various drivers. They are here for their vacation, and there is no chance that driver will not pick them up if they say "no thanks" instead of "mi not ready yet". A simple "no thanks" will work just fine.
As for taking a route taxi off their route - the fact she requested the diversion, the driver asks permission from the other passengers and then she paid an additional amount does essentially change the route taxi definition. They are no longer on their route and she is no longer paying just the route taxi rate. Thus is has become a charter by definition, albeit a short charter.
As for the bus park experience going to another town, once again, this is something that the vast majority of visitors to Jamaica would never need to worry about.
The red plate taxi is ALWAYS the way to go for visitors to the island.