Eric,
If you find that the short is in a secondary winding, and find which one it's in, perhaps you could eliminate that particular winding from the chassis connections. Then, if you happen to have another old transformer laying around that has a secondary winding with the same value or pretty close as your shorted winding, you could wire that one into the circuit where the shorted winding was.
This, of course will depend on a couple of other things... First, whether or not the short in the origional winding is within itself or possibly shorted to one of the other windings. This idea would only apply if the short is within one winding itself. Second, if you do have another transformer with a winding close to or the same as the shorted one, will the size of that transformer be too big to place somewhere in the cabinet since this will put two trasnformers in the set?
Man, that was a mouthful... did I get the idea across? Sometimes I can see something in my mind so clearly, but have trouble putting it in words!
You guys think this will work? Or would it cause other problems?