In a medium bowl, combine the vinegar, 1/4 cup sugar, and half of the garlic and chiles. Stir until sugar is dissolved. Add the carrots and let sit at room temperature for 1 hour for a quick pickling of sorts.
In another medium bowl, combine the lemon juice, tangerine juice, shallot, fish sauce, sambal oelek, and water. Stir in remaining garlic, chiles, and 1 tablespoon sugar. Mix until sugar is well dissolved. This is your dressing... and it's phenomenal.
In a large salad bowl, combine the mango, cucumbers, watercress, basil paste, and cilantro. Drain the carrots, shaking off any extra liquid, and add into the bowl as well. Stir in the dressing and toss well. Place big portion on large plates and top with lump crab meat. Garnish with the scallions and dig in!