GGR, your thinking parallels closely what I've been thinking. As far as 'what happened to the car giving its identity', if the VINs were swapped, that car would have benefitted by acquiring the identity of a more recent model.
A stolen car is another possibility that I've thought of. I agree with 66andBlue that 30 years ago, when this would have been done, changing the VIN on a stolen car, including the frame rail stamping, seems like more trouble than the car would have been worth at that time.
It's really hard to know which of these scenarios are more likely to be correct, without more information.
I did talk to Tom Hanson and he was puzzled by what I told him, but confirmed that the database can't be searched by engine number. He said he'd be really surprised if the VIN had been changed. He also said the datacards reside in Germany; they don't have a copy of the entire set in California; and certainly not ones from European cars.
I spent a bit of time on the registry and looked at VIN/engine number pairs. I thought I might be able to use that to narrow down the VIN of the car that would have had my engine number. However, it turns out that the engine numbers did not increase with the same regular sequence as the VINs...there's a fair bit of 'noise'. As a result, the best I can do is bracket the VIN to a range of about 1000. And if those datacards would have to be searched manually, it would take some time.
So at this point, I'm pretty much at a dead end. Apart from showing up at the Center in Fellbach and pleading for access to look through a thousand datacards, I don't see what else I could do.