Discard shiitake mushroom stems; cut caps into quarters.
Lightly spoon flour into a dry measuring cup; level with a knife. Combine flour, 1/2 cup crushed tomatoes, and thyme in an electric slow cooker; stir well with a whisk. Add all mushrooms, onion, and sun-dried tomatoes.
Trim fat from pork. Sprinkle pork with salt and pepper; place on top of mushroom mixture. Pour 1/2 cup crushed tomatoes over pork. Cover with lid; cook on high heat for 1 hour. Reduce heat setting to low; cook 7 hours. Remove pork from slow cooker; cut into slices. Serve over noodles.