Make the barbecue sauce: Combine all ingredients in a medium pot over medium-high heat. Cook, stirring occasionally, until boiling. Reduce heat to low and simmer until the guava paste has dissolved and the sauce has thickened, 10-15 minutes. Store in an airtight container in the refrigerator.
Make the chicken: Combine 1 cup guava barbecue sauce with the mustard and Worcestershire sauce in the bottom of a large slow cooker. Add the chicken breasts and toss to coat. Cover with lid and cook on high for 4 hours or on low for 8 hours. Shred the chicken and stir to combine with the sauce. Season to taste with salt and pepper.