To make the anchovy broth, combine the mushroom, anchovies, kelp, 4 cups water, and the salt in a medium, heavy-bottom pot, and bring to a boil. Reduce to a simmer and cook for 30 minutes. Remove from the heat, strain and discard the solids, and set the broth aside.
Place the SPAM, kimchi, rice cakes, onion, scallions, garlic, hot dogs, and pork in small separate piles in a large shallow pot.
Add the soy sauce, gochujang, gochugaru, and cheongju to the pot, then slowly pour in the reserved anchovy kelp broth. Add the baked beans and 1½ cups water. Bring the contents to a steady simmer over high heat, stirring occasionally with a wooden spoon.
Cook for about 10 minutes, then add the ramen noodles. Ladle the broth over the noodles to help them break apart. Continue to cook for 2 or 3 minutes, until the noodles are cooked through but still chewy.