Heat oil in a large nonstick skillet over medium-high heat. Sprinkle ribs with 3/4 teaspoon salt and 1/8 teaspoon pepper.
Add half of ribs to pan; cook 2 minutes on each side or until browned. Place ribs in an electric slow cooker. Repeat procedure with remaining ribs.
Add shallots, garlic, and ginger to pan; sauté 2 minutes. Stir in 1/4 cup water and curry paste; cook 1 minute. Stir in coconut milk, sugar, and fish sauce. Add coconut milk mixture to cooker. Cover and cook on LOW 6 hours.
Remove ribs from cooker; keep warm. Strain cooking liquid through a colander over a bowl; discard solids. Place a zip-top plastic bag inside a 2-cup glass measure.
Pour cooking liquid into bag; let stand 10 minutes (fat will rise to the top). Seal bag; carefully snip off 1 bottom corner of bag.
Drain drippings into a small bowl, stopping before fat layer reaches opening; discard fat. Stir in remaining 3/4 teaspoon salt, remaining 1/8 teaspoon pepper, rind, and juice.
Shred rib meat with 2 forks; discard bones. Serve sauce over ribs and rice.