Definitive Jerk Chicken
Are you beginning the cooking process (after the marinade) with a spice rub and then poking that spice into ("jerking") the meat? This is an obviously key step considering it's how the technique got its name, but I thought I might mention it. A good rub will go the distance, but like posts about buying chili powder and italian seasoning, make your own. Find one you like then build it from scratch. The 'definitiveness' is really in the cooking and the attitude of the fire. (Also, you list allspice, but don't mention if it is fresh ground; definitely make sure to do a fresh pass through the mortar and pestle and buy whole if possible... and you might add some coriander but that's more a complement than a jerk necessity.)

Working within the marinade, I would recommend steering away from the brown sugar a bit and incorporating a fruit juice like orange or any tropical fruit pulp. 

For an additional bit of emphasis on thyme: I am not sure how much you are digging into the cayenne/onion flavors, but the more you are the more thyme can also help lift the spirits of the dish and give its smokiness a brilliant contrast. Of note, too much thyme though and you will veer sharply toward cajun, for better or worse.