Sprinkle onion slices with coarse salt, and rub them between your hands until you no longer feel the salt. Drain onions in a colander 15 minutes. Wring out as much liquid as you can by squeezing small bunches of the slices in your fists.
Combine onions, pineapple, and next 7 ingredients in a large bowl. Combine olive oil and vinegar; toss with fruit mixture.
Grill shrimp 3 minutes on each side or until opaque, and immediately toss into the salad. Gently stir in avocado. Season to taste with black pepper.