Blend marinade mix, 1/4 cup of the broth and oil in bowl; spread evenly over both sides of beef. Place beef in jumbo resealable plastic bag; top with garlic and onion. Seal; refrigerate at least 8 hours or overnight, turning occasionally.
Preheat grill to medium indirect heat. Remove meat from marinade and place in large foil grill bag; discard marinade. Finely chop 1 chipotle pepper. In medium bowl, combine pepper with adobo sauce, 1/2 cup of the barbecue sauce, and remaining 3/4 cup broth; spread over beef. Fold and crimp edge of bag to seal, leaving room for expansion. Carefully place packet over indirect heat. Grill, covered, 3 1/2 to 4 hours or until meat is tender; remove from grill.
Finely chop remaining 3 chipotle peppers. Add peppers with adobo sauce to remaining 1 1/4 cups barbecue sauce in bowl. Carefully remove meat from packet, reserving juices. Place meat on direct medium heat; grill 6 to 8 minutes per side to sear, basting lightly with part of barbecue sauce mixture.
Meanwhile, skim fat from reserved juices. Gradually stir 1/2 cup juices into remaining barbecue sauce until desired consistency; set aside. Using 2 forks, shred beef; return to reserved juices. Serve, with any remaining barbecue sauce mixture, in warm tortillas.
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