Place cabbage, carrots, onion, scallions, garlic, salt, black pepper, paprika, and allspice in a large nonreactive bowl. Using your hands, mix thoroughly for 1 minute. Be aggressive; punch, massage, and pound the ingredients together. Stir in chiles. Let mixture stand, uncovered, at room temperature 6 hours, mixing and massaging every hour.
Transfer cabbage mixture and any accumulated liquid in bowl to a 1-quart wide-mouth glass jar. Add vinegar; press down vegetables to submerge. Seal jar; let stand at room temperature at least 8 hours or up to overnight.
Stir pikliz in jar. Pour pikliz through a fine wire-mesh strainer into a bowl, reserving solids and strained seasoned vinegar. Top each oyster with about 1/2 teaspoon strained pikliz. Reserve remaining pikliz and seasoned vinegar for another use. To store, recombine pikliz and seasoned vinegar in jar; seal and refrigerate.
Pikliz and seasoned vinegar may be stored together in an airtight container in refrigerator up to 3 months.