Combine first 7 ingredients in a large shallow dish or zip-top freezer bag; add steaks.
Cover or seal, and chill at least 2½ hours, turning occasionally.
Remove steaks, reserving marinade.
Bring marinade to a boil in a small saucepan; boil 1 minute.
Sprinkle steaks with salt.
Grill, covered with grill lid, over medium-high heat (350° to 400°), basting often with reserved marinade, 7 minutes on each side or to desired degree of doneness.