For the record--in case there are any more of these models out there!--here's how it worked out.
The KitchenAid people were very helpful, but all they had were installation instructions for a comparable model. From that I learned that the sink, sink cabinet, and dishwasher were originally installed as a "unit."
So, I gave up, figuring there were loads of attachment points that I just wouldn't be able to get to: the objective changed from replacing the dishwasher to rescuing the stainless steel sink and top.
It turns out, though, despite the claim on another Web site that "the dishwasher is secured to the cabinet with screws from the back, front, and through the side from underneath the sink,* that nothing could be further from the truth:
The counter and sink were held with screws beneath the front two corners and, in the back, with metal pegs designed to slide forward and up:
In this picture the counter has been turned sideways: you're looking at the original back right corner. The installer reinforced it with wood. I don't know whether the steel bar-and-peg assembly screwed to it is original or not.
- The diswasher itself was attached only with four screws to the cabinet at its left:
In the photo, looking down into the now-open sink cabinet, you can see the one remaining screw (upper left) and a hole for another (upper right). Two more screws were set in the bottom corners. That's all! In principle, you could remove this dishwasher by removing (or drilling out) these screws, cutting the water supply (sweated in place, of course), and pulling it forward. No part of this unit was attached to the floor or walls, either: it was free-standing.
By the way, to bring this story to a happy close, here is a photo of the new sink cabinet (partially constructed) with the old counter and sink restored, ready for the new dishwasher:
Because the counter is completely hollow--it is reinforced with two narrow longitudinal ribs underneath, but that's all--it was necessary to reinforce the front lip for strength and to have a mounting point for the new dishwasher. A 1.5" by 1.5" piece of poplar fit just fine.
(For those with sharp eyes and a knowledge of the electrical code: that little jury-rigged pigtail at the bottom was just a temporary setup to test the dishwasher before pushing it into place. It was well worth the peace of mind to see that everything worked without any leaks: I lost a joist in a previous house to a slow undetected dishwasher leak.)