Like Smokin' says.
Yep,the "jerk" folks really are more into marinades/bastes/rubs and really haven't gotten as much into injections ,as the pork and poultry folks around here.
The jerk powdered rubs,should incorporate into an injection.
You might be able to mix Grace,Walkerswood,or one of the other fine commercial bastes into an injection medium.
Maybe apple juice,if you have a coarse needle,and don't mind the needle marks?
The scallions,onions,scotch bonnets,fresh Thyme leaves,etc,that make up the traditional paste, might be more complicated,and cooking them onto the surface of the product lends a lot to the flavor /mouth feel,etc.
Maybe,because jerk is done on smaller pieces,i.e. chicken parts,pork chops,fish?
Can't say, in all the Island nations,I've ever heard of jerking a whole turkey.