Stir water, kosher salt, bay leaves, allspice, and black peppercorns in medium bowl until salt dissolves for brine. Arrange pork chops in 13 x 9 x 2-inch baking dish. Pour brine over. Cover and refrigerate 1 hour, turning occasionally.
For charcoal grill: Remove top rack from barbecue. Place 1 aluminum pan in center of lower grill rack for drip pan. Light briquettes in chimney; carefully pour onto lower grill rack, forming piles on either side of drip pan. Drain wood chips; scatter wood chips evenly over coals. Return top grill rack to barbecue.
For gas grill Remove top grill rack from barbecue. Prepare barbecue (medium heat). If using 2-burner grill, light 1 burner. If using 3-burner grill, do not light center burner. Drain wood chips. Stack 2 mini loaf pans (one inside the other); fill with 1 cup wood chips. Stack remaining loaf pans; fill with 1 cup wood chips. Place pans directly on flame (if using 3-burner grill, place both pans on 1 lit side). Place aluminum baking pan on unlit portion of grill. Return top grill rack to barbecue.
Grill onion quarters until browned (skin may burn), about 3 minutes per side. Cool and peel. Thinly slice and place in bowl. Add orange juice and lime juice. Season onion mixture to taste with salt. Mix in chopped cilantro.
Remove pork from brine; pat dry, then grill covered over drip pan until cooked through, 4 to 6 minutes per side. Transfer to plate; let rest 10 minutes.
Arrange cabbage on platter. Top with pork, avocado, and radishes. Drain onion; scatter over pork and vegetables. Sprinkle chopped cilantro leaves over. Serve with warm corn tortillas.