For crust, in a bowl stir together crushed crackers and the 1 tablespoon sugar; stir in melted butter. Press onto bottom of a 6x3-inch springform pan.
In a large bowl beat cream cheese with a mixer on medium for 30 seconds. Beat in the next three ingredients (through vanilla) until combined. Beat in sour cream. Beat in eggs on low just until combined. Stir in cherries and 2 tablespoons of the chocolate pieces. Pour over crust in pan.
Place a small rack in a 6-quart slow cooker. Add warm water to cooker to just below rack. Set springform pan on rack.
Cover opening of cooker completely with three layers of paper towels; place lid on top or cover with foil. Cook on high for 2 hours. Turn off cooker and let stand, covered, for 1 hour. Remove springform pan from cooker. Cool cheesecake on a wire rack for 1 hour. Cover and chill 4 to 24 hours.
To serve, loosen and remove cheesecake from pan. Top with pie filling. Melt the remaining 2 tablespoons chocolate pieces and drizzle over cheesecake.