Trim fat from meat. If necessary, cut meat to fit a 5- to 6-quart slow cooker. Place onions in cooker. Transfer meat to cooker. Sprinkle with salt and pepper. Add garlic, peaches, and ginger ale.
Cover. Cook on low-heat setting 8 to 10 hours or on high-heat setting 4 to 5 hours.
Remove meat to cutting board, reserving remaining mixture in cooker. Using two forks, pull meat apart into bite-size pieces. Return meat to cooker. Add drained tomatoes. Stir to combine. Keep warm on warm setting, if available, or low setting.
Line buns with lettuce leaves. Use a slotted spoon to spoon meat mixture on buns. Top with additional sliced peaches. Makes 20, 1/2-cup (plus bun) servings.