To luxflairguy: YES! I had noted the wheels and the clips, figured that was one area I didn't have to deal with for the moment. I wonder how long it would have taken me to realize that there had to be fasteners (too solid to be just a "tab-and-slot") and that the only place they COULD be was under (over) the wheels.
Getting the electrics out of the way (the cord could be original; the grommet certainly was) enabled a first cleaning with a hose nozzle, dishwashing liquid, and brushes. It still has a bit of "old dirt" smell, but that worked well enough to justify further and more sophisticated cleaning. The chrome parts, which I had assumed were rusted through, are almost as new except for some minor scrapes on the switch actuator.
This unit isn't really restorable unless somebody is reproducing the decals (70% gone before washing), and the original wrinkle finish is in poor shape and covered with drips and spatters of at least two colors of oil-base paint. I'll probably mask the chrome and give it a coat of good spray paint. But I bought it not as a collectible but as a first-class household tool. One that had belonged to my grandmother is long gone. In the year between the time I first looked on eBay and the time I bought this one for $50 (complete), prices had soared.
Again, my thanks.