Make 3 crosswise slashes down to the bone on each side of each fish.
In a food processor, process the chile, scallions, garlic, shallot, ginger, thyme, salt, brown sugar, allspice, pepper and cinnamon until a coarse paste forms.
Add 2 tablespoons of oil, the rum, lime juice, water and soy sauce and puree.
Arrange the fish in a shallow dish.
Stuff the cavities and slashes with the seasoning; refrigerate for 1 hour.
Light a grill.
If using fish baskets, lightly brush with oil and place the fish inside.
If using a fish grate, preheat it and lightly brush with oil.
Grill the fish over a medium-hot fire until cooked through, 8 minutes per side.