Coarsely grate tomatoes into a bowl and discard skins. Place onion and bell peppers in another bowl. Measure garlic, paprika, and salt into a small bowl. Place rice, seafood, and chorizo each in a separate bowl.
Toast saffron in a large saucepan over medium heat, stirring, for 2 minutes. Add 6 cups broth and the wine, cover, bring to a boil, and keep hot. In a small saucepan, boil remaining broth; keep hot.
Meanwhile, make the aioli: In a food processor, mince 4 garlic cloves. Add 1 large egg plus 1 large egg yolk, lemon juice, and 1 tsp. kosher salt; whirl to blend. With motor running, pour in 1 cup extra-virgin olive oil and 1/3 cup canola oil. Add more lemon juice and salt if you like. Chill until used. Makes 1 2/3 cups.
Heat grill to medium (350° to 400°). Bring prepped ingredients to grill, along with a long-handled wooden spoon, a slotted spoon, and oven mitts. For charcoal: Add 15 briquettes to fire just before cooking and cook with lid off until adding seafood. For gas: Keep lid closed as you cook.
Heat a 17-in. paella pan on grill. Add 3 tablespoons oil to pan, then brown chorizo, stirring occasionally, 5 minutes. Using slotted spoon, transfer chorizo back to bowl.
Sauté onion and peppers in pan until onion is softened, 5 minutes. Stir in tomatoes and cook, stirring often, until liquid evaporates and paste turns a shade darker, 10 to 12 minutes. Stir in the remaining 1/4 cup oil and the garlic mixture; cook, stirring, for 30 seconds. Stir in rice, then pat it level.
Carefully pour hot saffron liquid over rice and scatter chorizo on top. Adjust position of grill if necessary so grill and liquid in pan are level. Maintain a steady simmer for 12 minutes, reducing heat (for gas) or airflow through vents (for charcoal grill) if needed.
And finally, add the seafood: Pour enough hot plain broth over paella so rice is just covered. Arrange mussels around rim of pan, almost touching, pushing them into liquid. Distribute remaining seafood over paella.
Cover grill. Cook until clams and mussels open and rice is al punto (al dente), 6 to 10 minutes. Remove paella from grill, drape with paper towels, and let stand about 5 minutes. Scatter parsley and/or green onions on top. Serve with the aioli.