Line a 4-cup coeur à la crème mold with a double layer of damp cheesecloth; allow cheesecloth to extend over edge of mold.
Place first 5 ingredients in food processor, and process until smooth. Sprinkle gelatin over water in a small saucepan; let stand 1 minute. Cook over low heat, stirring until gelatin dissolves. Remove from heat; let cool slightly. Add 1/4 cup cheese mixture to gelatin mixture, stirring with a wire whisk; add to remaining cheese mixture in processor, and process 1 minute. Spoon cheese mixture into prepared mold. Fold cheesecloth over top of cheese mixture; place mold in a shallow dish, and chill at least 12 hours.
To serve, unfold cheesecloth, and invert molded cheese mixture onto a serving plate; remove cheesecloth. Serve with berries and gingersnaps.