For filling, bring ¾ cup of water and vegetable oil or butter up to a boil. Stir in brown rice, reduce heat to very low (so that water is barely simmering), cover and cook until all liquid is absorbed, about 20 minutes. Set aside.
In a large pan with 2-inch sides, add pork, beef, onion and carrot. Cook over medium heat, stirring often, until meat is cooked, about 15 minutes. Drain away any fat, then stir in paprika and celery salt. Stir cooked rice into meat mixture and season to taste (season highly, as salt and other seasonings will cook out into the cabbage and sauce later). Cool enough so that it can be handled.
For assembly, preheat oven to 375 °F. Bring a large pot with water to a full boil and salt. Peel away cabbage leaves carefully, to keep them as intact as possible. Blanch leaves in water in batches of 3-4 leaves, until just soft enough that it is pliable (about 3 minutes for outer leaves, 2 minutes for inner leaves). Place blanched leaves on a baking tray.
To roll cabbage rolls, lay out a cabbage leaf and trim out stem with a paring knife. Depending on the size of the leaf, cut into 2 or 3 pieces. Spoon a heaping tablespoonful of cooled filling onto each leaf portion (press filling with your fingers to compact it a bit). Fold cabbage over filling and roll as tightly as possible without tearing cabbage. Repeat with remaining cabbage leaves.
Spread half of sauerkraut in the bottom on a large casserole. Arrange cabbage rolls on top (you can layer cabbage rows in 2 layers, if your pan is too small to fit all in 1 layer). Top cabbage rolls with remaining sauerkraut and pour crushed tomatoes overtop, tucking in bay leaves and seasoning. Pour water into casserole, so that it comes halfway up the cabbage rolls (give the dish a shake to let all the liquid settle in). Cover dish and bake for an hour at 375 °F, then reduce oven temperature to 350 °F and cook another hour. Let cabbage rolls sit for 15 minutes before serving.
Alternatively, cabbage rolls can be assembled into smaller dishes and frozen before baking.