Cut habanero in half. Seed one half of pepper, and leave seeds in other half. Mince both pepper halves. Combine minced habanero, orange juice, 1/4 cup lime juice, minced shallots, and next 5 ingredients (through thyme) in a large bowl; stir with a whisk. Add pork; toss to coat. Cover and chill 12 to 24 hours.
Place pork and marinade in a Dutch oven over medium-high heat. Add broth; bring to a boil. Cover, reduce heat, and simmer 1 1/2 hours or until meat is tender. Remove pork from pan with a slotted spoon, reserving cooking liquid. Strain cooking liquid through a sieve into a bowl; discard solids. Place a large zip-top plastic bag in a bowl. Pour reserved cooking liquid into bag; let stand 5 minutes. Snip off 1 bottom corner of bag; drain liquid into a medium saucepan, stopping before the fat layer reaches the opening. Discard fat. Set 1/2 cup cooking liquid aside.
Place saucepan with cooking liquid over medium-high heat; bring to a boil. Cook 20 minutes or until reduced to about 1 cup. Add sliced shallots, vinegar, black pepper, and 1 tablespoon lime juice. Cover and keep warm.
Heat oil in a large nonstick skillet over medium heat. Add pork; cook 10 minutes, turning to brown well on all sides. Add reserved 1/2 cup cooking liquid and remaining 1 tablespoon lime juice. Increase heat to medium-high; cook 4 minutes or until liquid nearly evaporates, stirring occasionally. Place pork in a bowl; pour sauce over pork.