Begin the bread by softening the yeast in the water in the bowl of a mixer with the hook attachment. Give the yeast about 5 minutes to bubble up (to know it's working).
Add the shortening, rye flour, 1 cup of the AP flour, salt, honey, and caraway seeds. Beat on low speed for about 2 minutes.
Gradually add more of the remaining AP flour, 1/4 cup at a time, until the dough forms a mass and begins to pull away from the side of the bowl.
Knead on low speed, adding more flour a little at a time as needed to prevent sticking, for about 8 minutes.
Add about 1 tsp of neutral oil to the bowl and roll the dough around to coat. Cover with plastic wrap and let rise about one hour or until double in size.
Turn the dough out onto a lightly oiled work surface and roll out into a 10 x 25-inch rectangle.
Make the filling by combining the Thousand Island dressing, mustard, drained sauerkraut, corned beef and 2/3 of the Swiss cheese. Spread the mixture evenly on the dough leaving a 1 inch border along the top 25-inch edge. Starting from the bottom 25-inch edge, roll tightly toward the top. Pinch the seam together and tuck each end under. Coil the dough loosely and put onto a well-greased (or nonstick) pan. Cover with a towel and let rise for about 45 minutes or until almost double in size.
Half an hour before the end of rising, preheat the oven to 375 degrees F.
Just before baking, top the coil with the remaining Swiss cheese. I cut into triangles and lay out along the length though it's just as easy to sprinkle on shredded Swiss if that's what you are using.
Bake for 35 to 40 minutes or until golden brown.
Remove from the pan and let cool on a rack for at least 20 minutes before serving in wedges.