There are no specific instructions for the repair that I am aware of since a repair of that type would normally be done by a professional who would rely on their training and experience.
If you do want to tackle the job yourself, you can use the parts diagrams in your manual or on the Sears PartsDirect site as a guide. See the image below from the site for an example. Those illustrations will not show any specific repair or provide instructions but they are the same ones technicians use during their repairs and with careful review you should see the parts involved and roughly how they fit and work together.
Looking at exploded-view for the auger housing, reference key number 500; it looks like two separate pieces but as you noted it is actually one solid welded piece and only shown separated for a clear view of other parts. The only way to handle the loads faced on a model of this size is to make the auger housing a one-piece assembly. That means the auger shaft, gear case, and impellor shaft all have to be removed before you can swap the augers. And that is what stops this from being a quick and easy repair.
The basic steps are to remove the bearings/flanges from the auger housing on either end of the auger shaft, see key 525. Then remove the pulley, key 480, and bearing/flange, key 490, from the backside of the impellor shaft. At that stage the whole gear case assembly with the shafts can come forward out of the housing. The impeller is held on to the shaft with spring pins. They have to be knocked out with a punch. Sanding the shafts will aid in removal.
If you do not feel confident repairing this problem yourself, then you can have it repaired at your home by a Sears technician. Here is a link for the website:
Sears Home Services