Crumble ground venison and ground beef into bowl of a heavy-duty mixer; sprinkle with 2 teaspoons salt, pepper, and allspice. Add 1/4 cup onion and next 5 ingredients; mix thoroughly at low speed. Shape mixture into 1" meatballs.
Heat oil in a large skillet over medium-high heat until hot. Add meatballs in batches, and cook until browned, turning often. Remove meatballs from skillet with a slotted spoon; set aside and keep warm.
Cook chopped onion and celery in pan drippings until golden. Add chopped garlic; cook 30 seconds. Reduce heat to medium; stir in tomato paste. Cook until paste begins to brown. Stir in cherries and next 6 ingredients; cook over medium-high heat, scraping bits that cling to bottom of skillet. Bring mixture to a boil, and cook until liquid is reduced by about half. Add broth; return to a boil and cook 15 minutes or until liquid is reduced to 2 cups. Remove from heat; cool slightly, and discard bay leaf and thyme sprigs.
Pour sauce into container of an electric blender; cover and process until smooth, stopping once to scrape down sides. Pour mixture back into skillet through a wire-meshstrainer. Add meatballs to cherry sauce. Bring sauce to a boil; reduce heat and cook, stirring occasionally, until meatballs are thoroughly heated. Transfer meatballs and sauce to a chafing dish. Serve warm with wooden picks.