Combine first 4 ingredients in a large bowl, stirring until the salt and sugar dissolve. Pour salt mixture into a 2-gallon zip-top plastic bag. Add ice and pork; seal. Refrigerate 3 hours, turning bag occasionally.
Combine paprika and next 5 ingredients (paprika through garlic).
Prepare grill for indirect grilling, heating one side to medium-high and leaving one side with no heat.
Remove pork from bag, and discard brine. Pat pork dry with paper towels. Brush oil evenly over pork; rub with paprika mixture. Place pork on grill rack coated with cooking spray over medium-high heat; grill pork 6 minutes, browning on all sides. Place pork on grill rack over unheated side. Close lid, and grill pork an additional 20 minutes or until thermometer inserted into thickest portion of pork registers 155° (slightly pink), turning the pork occasionally. Place pork on a platter. Cover with foil, and let stand 5 minutes. Uncover and drizzle pork with 2 teaspoons vinegar.
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