OK! Here's the answer:
In the front of the tractor are the front support hangers. Essentially, they are two slots that the front draft link pivot pin slides into. When the pin is all the way in the two slots, the rear lift arms are all the way in the rear lock assembly.
In this case, the right-hand front support hanger was bent! The bend prevented the pivot pin from sliding all the way back. The local dealer's repair guy was able straighten the hanger out with really big crescent wrench.
Now the mower installs correctly under the tractor.