Add pork, 2 quarts beef stock, mushrooms, onions, garlic, celery, carrots, tomatoes and bloody mary sauce to the slow cooker. Secure lid and cook on low for 7½ hours.
Add remaining beef stock and rice to a saucepan over medium-high. Cover with lid and cook for 18 minutes. Remove from heat, but do not remove lid. Leave until ready to serve.
Remove pork from slow cooker and chop into bite-sized pieces. Remove ½ cup of stock. Return pork to slow cooker. Mix cornstarch with stock with a fork and add slurry to slowcooker. Stir to combine and secure lid for 15 minutes.
Add portion of rice to a shallow bowl and ladle stew over top.