Okay, I tried a few things based on your suggestions. First I used the scenario editor to bulldoze and replace the auto plants. The result was that the north auto plant promptly built 4 lots of automobiles! Unfortunately, it then went back into idle mode and refused to build any more. Bulldozing and replacing it again didn't make it build more, either.
I tried bulldozing Auto City's buildings so that it doesn't lure away supplies from the auto plants, but it didn't seem to make any difference. I also set up a train running cargos back from Auto City to the auto plant, but since the auto plant won't actually use them, they end up going around and around in a circle.
I tried focussing on the one auto plant - bought it, upgraded it, and rearranged my trains to supply the materials in much larger quantities - and noticed something odd. The auto plant will stack up supplies of steel, textiles, rubber, machinery and glass, but NOT electronics. Also on the cargo map, there is no blue demand arrow on the plant for electronics, though there is for everything else. When trains deliver electronics, the plant seems to ignore them and they migrate away overland to the city. (Where the train promptly brings them back again...) I wonder if this is the source of the problem? The plant needs electronics to produce automobiles, but doesn't 'demand' them?
This has been a fun scenario, setting up all the various industries and feeding materials in, but not being able to make the final product is very frustrating!