For the barbecue sauce:
Heat the oil in a large skillet over medium-high heat for 1 minute. Reduce the heat to medium and add the onion, cooking until it's soft and a little brown around the edges, about 5 to 7 minutes, stirring often. Stir in the guava paste, tomato paste, vinegar, brown sugar, star anise, allspice, and curry powder. Simmer until the guava paste has melted, about 15 minutes, stirring occasionally. Turn off the heat and let the sauce cool slightly. Discard the star anise; transfer the mixture to your blender and puree. With the motor running add the lime juice and rum. Transfer to a small bowl and set aside, or refrigerate for up to 2 weeks.
For the salsa:
Whisk the olive oil, garlic, lime juice, salt and pepper together in a large bowl. Add the mangoes, peppers, red onions, chile, and cilantro and toss to coat. Add the beans and gently toss everything together.
For the salmon:
Heat your broiler to high. Line a large flameproof baking dish or rimmed flameproof baking sheet with a double layer of aluminum foil and grease the foil with some olive oil or nonstick cooking spray.
Place the salmon in the prepared baking dish and tuck about 2-inches of the tail end under the fish, so you have a somewhat uniform shape. Pour the barbecue sauce over the salmon and cook it under the broiler until the sauce caramelizes and chars around the edges and the salmon is firm and flakes easily, 8 to 12 minutes for rare (the salmon will still be pink in the middle) or 12 to 15 minutes for well done (the salmon will be cooked throughout).
Spread the salsa on the serving platter and carefully lift the salmon out of the baking dish and arrange it on top of the salsa (use 2 large spatulas to transfer it). Squeeze a few lime wedges over the fish and serve with additional lime wedges on the side.