Put some charcoal in the center of the bottom of a large kettle grill. Light the charcoal, and place the grate on and cover the grill, let burn until the briquettes turn mostly gray.
Place the sausage on grill and cover with lid. Grill for 3-4 minutes until grill marks appear. Remove to sheet pan.
Brush the chicken with some of the olive oil and sprinkle with salt and pepper. Place the chicken skin-side down on outer edge of charcoal, and place the lid on. Cook the chicken until golden brown on both sides and leaving slightly rare. Remove and place on a sheet pan. Rest for 10 minutes and halve each thigh.
Combine the chicken stock, Old Bay seasoning, and saffron in a medium saucepan and bring to a simmer. Add the clams, cover and cook until the clams open. Remove the clams to a bowl. Add the mussels to the broth, cover and cook until the mussels open. Transfer to bowl Add the crab legs to the broth, cooked uncovered until the shell is bright red. Transfer to a bowl. Discard any shellfish that don't open.
Brush the shrimp and the cut sides of the lobsters with some of the oil and sprinkle with salt and pepper on all sides. Grill for 1-2 minutes. Remove the seafood and place on a sheet pan.
Heat the remaining oil in a medium paella pan placed directly on the grate over the coals. Add the onions and cook until soft. Add the garlic and cook a few more minutes.
Add the rice and cook, stirring for a few minutes. Begin adding the stock 1 cup at a time (reserving 1/2 cup for later) and tomatoes 1/2 cup at a time and cook, stir occasionally, allowing some moisture to asorb before adding more. Add the paprika and hot pepper sauce. Stir to combine until the rice is al dente.
Arrange the chicken, clams, mussels, shrimp, lobster and crab legs into the rice. Squeeze the juice from 2 of the lemon wedges over the top, and nestle the remaing wedges into the rice. Pour the reserved broth over the mixture, and sprinkle on the parsley.