Combine salt, honey, water, and coconut milk in a gallon-size zip-top bag. Add pork roast and toss to coat; refrigerate 2 1/2-3 hours.
Drain pork and pat dry with paper towels. Discard remaining brine.
Combine ketchup, vinegar, oil, and soy sauce. Toss pork roast in mixture and place on a roasting rack in a roasting pan.
Combine remaining ingredients and press into all sides of pork. Insert a probe thermometer into the center and bake in a 425°F (220°C) oven until internal temperature reaches 140°F (60°C) for medium rare.
Move to a plate and let rest 7 minutes. Serve warm with sweet and sour sauce on the side.