... or something like "Pollo adobado jamaiquino/jamaicano" with or without "estilo 'jerk'" added at the end.

“Jerk” here refers to a Jamaican style of preparing meat; it has nothing to do with "tirón," which can be another meaning of jerk:

Jamaican Jerk Foods: Jerk is the process of spicing and grilling meats, poultry, and even vegetables, although the most popular are jerk pork and jerk chicken. The resulting food yields a spicy-sweet flavor and a tender texture. Jerk is also used as a noun when describing the dry or wet seasoning mix used to jerk a particular food. Jerk shacks thrive on the side of the road in Jamaica as a local fast-food industry. (http://homecooking.miningco.com/library/weekly/aa080497.htm)

It can be used in Spanish, as in the following examples, but if you do, it would probably be best left in quotation marks.

de curry y coco. Reggea Satays de Pollo Banderillas de pollo con salsa jamaiquina estilo "Jerk". Carpachio Neptuno $75 Frescas finas laminitas de Salmón y ...
www.elbrunch.com.mx/beachclub.html

coco, escalonio y pimientos) y un pan redondo llamado bammy, hecho de yuca. Otro plato singular es el pollo o cerdo seco estilo jerk y marinado en pimientos. ...
www.amadeus.net/home/dest/es/america/jamaica/gastro.htm

ANTES DE COCINAR - 2 ADOBO JAMAIQUINO "JERK" Ingredientes: 1 media cebolla, finamente picada 1 ... todo. Es genial para el pollo. Adoba durante al menos cuatro horas ...
www.terra.cl/entretencion/especiales/dia_padre_2001/guythin...

Hope it helps.