Since no one took a stab at evaluating my hypothesis, I ran it by the guru at my favorite local computer shop and ordered an external DVD drive. It was delivered today and I've just installed it and tested my hypothesis.
It works exactly as anticipated, at a nearly trivial price, so now the DVD drive built into my computer can remain permanently set to region 1 and the external DVD drive can remain permanently set to region 2. Although I might occasionally forget and insert a disc of the wrong region, the software for each drive will display a warning and ask if I want to change the region. It will also display the number of changes remaining before the region is permanently set to the last region selected, so it protects me from my own absentmindedness, as well.
Marianna